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PHILOSOPHY 



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1918 






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FOOTNOTES 
FORMAL LOGIC 



by ,y^ 

CHARLES H.'rIEBER 



z m8J 



US* 



THE LIBRARY 

OF CONGRESS 

WASHINGTON 



CONTENTS 

PAGE 



Preface 



CHAPTER I 
Modern Indictment of Formal Logic S 

CHAPTER II 
Apprehension. Question and Assertion 31 

CHAPTER III 
The Import of Judgment 46 

CHAPTER IV 
Negation and the Infinite Judgment 68 

CHAPTER V 
Nature of Inference 81 

CHAPTER VI 
Immediate Inference 103 

CHAPTER VII 
The Case Against the Syllogism 122 

CHAPTER VIII 
Novelty and Identity in Inference 147 



PREFACE 

The psychologist, on the one hand, and the metaphysician 
and the episteruologist, on the other, have crowded our present 
day discussions in the field of pure logic into a very narrow and 
uncomfortable position. No sooner does the logician raise the 
question as to the origin and nature of the thinking process, 
than the psychologist warns him that he is trespassing in fields 
not his. Especially is this true when we venture to discuss such 
questions as the process whereby judgment develops into infer- 
ence or is depressed into conception. This we are told is not 
logic, but genetic psychology. On the other hand, when the 
logician raises the question as to the nature of knowledge in gen- 
eral, he is again rebuked for passing into the domain of meta- 
physics, epistemology or ontology. It has been said that if the 
logician should accept these restrictions which his neighbors have 
imposed upon his field, there would be little left of logic, except 
a mere collection of misleading formulae coupled with a little ele- 
mentary grammar. 

I think the situation is not quite so desperate as this, and I 
hope in some small measure in these studies to justify the present 
tendency to widen the field of logic. "When we attempt to define 
the nature and scope of logic, or of any other of the philosophical 
sciences, we find our inquiries passing by imperceptible steps 
from one field to another until presently each subject in turn 
claims to be the whole of philosophy. I believe it to be a mis- 
take to divorce logic — even for educational purposes — from the 
other philosophical sciences. I do not see how it is possible to 
answer the questions that are more than ever today besetting 
logical doctrine until we have first settled some of the funda- 
mental problems of philosophy. Formal Logic is again on trial 

[5] 



FOOTNOTES TO FORMAL LOGIC 

for its life. Iii recent years, at Least four* important volumes 
have been entirely devoted to this modern indictment of tradi- 
tional logic. Saving now for some fifteen years been charged 
with the responsibility of teaching Formal Logic, and to more 
than half a thousand students each year, I feel morally neces- 
sitated, as one of the humblest of the disciples of Aristotle, to 
give some justification for the faith that is in me. 

In the introductory pages of his Formal Logic, Professor 
Schiller remarks, in a somewhat disheartened mood, "it is not 
unlikely that this whole revolt will come to nothing and that 
Logic will continue to be taught on the traditional lines." He 
takes comfort, however, in the belief that the failure of the 
reform movement will not be due to any intrinsic error or weak- 
ness in the movement itself, but to the fact that the prestige of 
tradition is so overwhelming, the force of habit so insidious. 
Dr. Mercier in the preface to his New Logic also expresses gloomy 
misgivings as to the fate of his volume. He says "by the time 
the New Logic has stood two thousand years ... no doubt it 
will have had all the guts taken out of it." I think, however, 
that no serious attempt will be made to disembowel his book. Dr. 
Mercier has been disappointed, so he says, that none of the older 
writers, Bosanquet, for instance, have replied to his criticisms. 
It seems more likely therefore, that his volume will be allowed 
to dry up with its entrails in it and become an interesting object 
for antiquarian research in the generations to come. 

I have chosen the title Footnotes to Formal Logic for these 
studies, rather than the more pretentious title Logical Theory, or 
Principles of Logic, in order that I might convey my own con- 
sciousness of their incompleteness and shortcomings. But, while 
the collect ion of essays is by the title confessed to be fragmentary, 
I hope I have made plain a thread of continuity running through 
them all. I have not attempted to present a brief for Formal 



killer, V. C. B., Formal Logic, London, Macmillan, 1912; Sidgwick, 
A., Elementary Lotpr, Cambridge, University Press, 1914; Dewey, John, 
Essays in Experimental Logic, Chicago, University of Chicago Press, 191(5; 
Mercier, Charles, .1 New Louie, Chicago, Open Court, 1912. 



PEE FACE 7 

Logic that is without qualification ; for I have at times said some 
severe things about the ancient system. However, I think on the 
whole my efforts will be regarded as a defense of the Traditional 
Logic, and to that I shall not object. For, to use a very apt 
phrase of Dr. Mercier, if I have to choose between the New Logic 
and the Old Logic, I should "plump for'' the latter. 



CHAPTER I 

THE MODERN INDICTMENT OP FORMAL LOGIC 

I. 

The new theories of thought all make a common criticism 
upon the old idealistic Formal Logic. Whether we call these 
modern theories of knowledge pragmatic, realistic or empirical, 
matters little for our present purpose. They all agree in saying 
that the conceptual, a priori logic has never undertaken to set 
forth the conditions out of which actual thought has arisen ; nor 
has it defined the principles that estimate the success of thought's 
accomplishments. It has no theory of the whence and the 
whither of thought. "What we have to reckon with,*' Professor 
Dewey writes, "is not the problem of How can I think iiber- 
hauptt but How shall I think right here and now? not what is 
the test of thought at large, but what validates and confirms this 
thought." 1 

I wish to submit at once, and it will be one of the central con- 
tentions of these studies that it is unfair to the formal logician, 
even of the old orthodox type, to say that he is unwilling to take 
notice of the concrete facts, that he has a contempt for the parti- 
culars, that the universals are more precious to him than the 
particular cases to which they apply. Only a hasty and reckless 
idealist affirms any such doctrine. An essential part of thought 
is always engaged in the effort to reach final truths — propositions 
that are not merely finally true in the sense of being a complete 
and adequate adjustment to an immediate situation, but truths 
thai are certain and universally valid. Even the most zealous 
defender of the modern "flowing philosophy" admits the exist- 
ence of this logic iiberhaupt, alheit, he insists that it is a useless 



i Studies in Logical Theory (University of Chicago Press, 1903), p. 3. 

[8] 



THE MODERN INDICTMENT OF FORMAL LOGIC 9 

pursuit. Another part of thought, which regards itself just as 
essential, attempts to arrive at practical truth ; it is concerned 
with the reconstruction of the "immediate situation." Now, 
Experimental Logic asserts its competency to pass judgment not 
only upon its own pragmatic process, but also upon the episte- 
mological aspirations of the Real Logic. And it is to this basic 
doctrine of the new school that the old school registers its earnest 
caveat. 

The idealism represented in these pages is of a very old- 
fashioned type. It essays to defend even so abstract an idealist 
as Plato against the assaults of the modern realist. 2 It has often 
been said that the logic of Platonism, or any absolute idealism, 
drives one either to pure intellectualism or to pure mysticism. 
But even Plato did not put the whole emphasis in his thinking 
on the theory of knowledge. Philosophy was for him, to be sure, 
primarily a discipline of the mind ; but it was a discipline which 
ended always in the service of action ; it was the propaedeutic 
for character. Thought was quite as pragmatic for Plato as it is 
for any of the modern voluntarists, only it was pragmatic, I 
should say, in a thoroughly defensible sense. The mind 's essential 
nature is exhibited in its everlasting aspiration after truth. But 
perfect insight, genuine wisdom, has as its essential characteristic 
the inevitable necessity of expressing itself. The knowledge that 
the mind wins must flow out into character. Man 's complete life 
consists not only in thinking perfect thoughts, working them out 
like nuggets of gold, but also in coining them into action. Plato 
insisted always that Logic is the absolutely indispensable pre- 
requisite of Ethics, and, conversely, that Ethics was the inevitable 
outcome of Logic. 



2 In these studies I shall often speak of instrumentalisni, realism, and 
pragmatism as if they were identical doctrines. I am, of course, fully 
aware of the several points of vital difference which have been insisted 
upon by various members of the two schools. But for the purpose of the 
contrast with idealism we may neglect these differences and deal with their 
central agreement. Both realism and instrumentalism declare that think- 
ing is instrumental or reconstructive and not constructive, as idealism 
always professes. They hold that thought finds real brute existences in 
the world of presented fact — structures that are not created but discovered. 



10 FOOTNOTES TO FORMAL LOGIC 

Logic in the fullest sense of the word is therefore the source, 

but not the final goal of the Platonic philosophy, or of any serious 
idealism, [nsighl is not for its own sake but for the sake of action. 
Knowledge turns not inward upon itself, but outward upon con- 
duct. It is practical; it is pragmatic. According to the sublime 

Platonic formula of life (even in its most modern interpretation 
by Caird, Royce, Eowison and others), knowledge is virtue, not, 
knowledge is knowledge. Plato w r ould have agreed entirely with 
a modern up-to-date metaphorical epigram; "knowledge that 
turns inward upon itself creates a current so hot that it burns 
out the fuse." 

Knowledge begins with surprise and ends in the rational dis- 
sipation of surprise; it is original, underived, reminiscent. This 
is the basic doctrine of Plato's philosophy which has been echoed 
and reechoed through twenty-three centuries of idealism. But 
now we must bear in mind that it is not pure wonder, just un- 
alloyed surprise, but rather a troubled wonder that is the source 
of knowledge. We are not and cannot be just the passive happy 
spectators of a stream of fugitive impressions flitting across the 
stage of consciousness. The presentations from the sense world 
come as competing alternatives. This it is very important to 
remember in considering any conceptual logic. The Platonic con- 
ception of wonder has lent itself to poetic imagination and strik- 
ing rhetoric, but it is a misunderstanding of it that makes it syn- 
onomous with pure reverie, mystic contemplation. Consciousness 
is not merely passive, it is essentially active. All waking con- 
sciousness is one continuous affirmation, an affirmation which, 
to he sine, always expresses itself in a disjunctive judgment, 
as we shnll src later. Now Plato insisted — at times with almost 
indignant emphasis — that sense presentations are incapable of 
thickening up into any final meaning, or validity of their own. 
Objects of sense perception are always particulars. And no 
accumulation of particulars by sheer juxtaposition or association 
can yield true knowledge. An aggregate of particulars is just 



TEE MODEEX IXDICTMEXT OF FORMAL LOGIC 11 

another particular. Knowledge presupposes universals. There 
is, therefore, a world of ideas above this world of fleeting sense 
perception. And the mere beginner in the study of Platonic 
philosophy knows that the ideas are entities, genuine objects of 
knowledge, and that they must never be taken as states of con- 
sciousness merely. 

The New Logic cancels the distinction between origin and 
validity, between what we discover about a particular fact through 
an analysis of its present content, and what we learn about it by 
an historical study of the conditions of its birth and development. 
Professor Dewey 3 says of the orthodox logician : ' ' He deals with 
the question of the eternal nature of thought and its eternal 
validity in relation to an eternal reality. He is concerned, not 
with genesis, but with value, not with a historic cycle, but with 
absolute distinctions, and relations"; and again: "We have no 
choice save either to conceive of thinking as a response to a specific 
stimulus, or else to ' regard it as something ' in itself, ' having 
just in and of itself certain traits, elements, and laws. If we 
give up the last view, we must take the former." 

It is an engaging and important question which instrumental 
Logic asks, How does empirical science come by its general 
principles, and particularly how does it prove them? But the 
idealistic Logic has always insisted that this is not the same as 
the determination of the principles of knowledge. If the New 
Logic intends merely to assert that we never reach a conclusion 
unless we have already come by it through experience, no idealist 
will take exception. There is a deep truth in the assertion that 
we believe first and prove afterward or not at all. We do not 
know because we have reasoned but we reason because we know. 
Kant was very explicit on this point. He says, "Logic, on the 
contrary, being the general propaedeutic of every use of the 
understanding and of the reason, can not meddle with the 
sciences, and anticipate their matter, and is therefore only a 



3 Studies in Logical Theory, p. 14. 



L2 FOOTNOTES TO FORMAL LOGIC 

universal Art of Reason, the art of making any branch of knowl- 
edge accord with the form of the understanding. Only so far 
can it be called an organon, one which serves not for the enlarge- 
ment, hut only for the criticism <t)i<l correction of our knowl- 
edge."* 

1 need only refer to a significant fact thai has been pointed 
out frequently, namely, that several different meanings — some of 
them quite diametrically opposed — have been given to the term 
"practical'' as applied to judgment. Even the pragmatists who 
may now be said to have appropriated to themselves the "trade 
mark" of the term practical, seem to differ widely in their 
definition of it. In Kant's distinction between theoretical and 
practical reason, the theoretical reason is always practical, or 
pragmatic, although certainly not in the sense in which the word 
is tin ployed in some of the recent theories of judgment. When 
the pragmatist declares that all judgments are practical, does 
he mean to assert that the object of the judgment is created in 
the act of judging? The question as to precisely what the 
expression "creates its own object" may mean — the question 
upon the answer to which depend so many vital issues in Logic — 
will be considered more fully in a later chapter in dealing with 
the postulated objectivity in thought. I wish only to say, in 
passing, that this creative activity is the essence of all the 
alleged theoretical judgments in any type of idealism, even the 
most ancient. The primary object of the Critique of the Pure 
Reason was to show that thought does actually create its object ; 
or, the least we max- say, is that it assists in its creation, in so 
far as it supplies the form that matter must take in knowledge. 

Any Logic that regards all judgments as practical labors 
under this inherent difficulty. How can any concrete, particular 
instance of knowing hope, at one and the same time, to create a 
valuable object and to know its creation as valuable. I am 
restating, I know, a very familiar and old criticism of prag- 



4 Introduction f<> !,<>!/><■; translated by T. H. Abbott (London, Long- 
. L885), j». 3. 



THE MODE EX IX DICE ME NT OF FOEMAL LOGIC 13 

matism when I say that value cannot be regarded as the hidden 
worth within a situation, which needs only to be brought to light, 
or evaluated. Value is not the self-determined issue of facts. 
Value proceeds from the activity which relates particular to 
universal, fact to law. The world of value is beyond the world 
of fact in the same sense that the straight line is beyond the curve 
which it determines. 

Pragmatic logicians are over-filled with the spirit of natural 
science. This they say, begins with practical definitions and 
follows practical methods to practical conclusions. Natural 
science has come to have such an enormous place in the common 
life, as well as in the academic world, that we can readily see 
how the Xew Logic has come by its over-weaning sense of the 
importance and certainty of the scientific method. The enthu- 
siastic devotees of natural science easily win the approbation 
of the fickle public, when they contrast the definite advance 
which the so-called pragmatic sciences have made, with the con- 
fusion and dispute which we seem still to find in the world of 
speculative Logic. The experimental logician insists that the 
difficulty with all the philosophical sciences — and not less so 
with Logic than with any of the others — is that they are all 
destitute of either accurate, initial definitions or certain methods, 
for the solution of their problems. The analysis and the evalua- 
tion of judgments of practice without external points of orienta- 
tion would be as difficult as the determination of a system of 
conies without the axes of reference. The conditions of asser- 
tion are manifold — sometimes operating singly, but for the most 
part combined in amazing complexity. 

It is the task of practical thought (upon this point the idealist 
agrees entirely with the pragmatist) to determine in what meas- 
ure each of the antecedents enters into the joint effect. The 
difficulty in accomplishing this task is the same as the difficulty 
that we meet elsewhere in the inductive sciences, for example, in 
the application of Mill's Method of Agreement. There the plur- 



li FOOTNOTES TO FORMAL LOGIC 

ality o\' causes renders the causal determination uncertain. And 
as in the world of outer natural sciences we find plurality of 
causes and intermixture of effects so in the world of inner 
natural science we discover each phenomenon to be the meeting- 
point of converging strands of conditions coming out of the past 
and diverging strands of effects going out into the future. They 
are like the knots in a net into which and from which various 
cords run. All of this is a most interesting study in Psychology 
bu1 it is not Logic. However cleverly phenomenena may be 
explained as the cross-section of the evolutional series, that is, 
as the meeting-point of forces, there still remains to be explained 
the essential identity or form of the whole. 

II 

Every act of thought is in the first instance an immediate 
presence, but it is also embedded in a continuum. This con- 
tinuum, in its entirety, is reality. It includes the present think- 
ing, and it is or may be the object of that present thinking. We 
have illustrated here the axiom of higher mathematics that the 
part can be put into a one to one correspondence with the whole 
of which it is a genuine part. On this point I should differ from 
Professor Dewey in the central thesis of his system that "think- 
ing is set in a continuum which is not an object of thought." 5 
On the view which I am presenting it is evident that the term 
nality is not so "particularly treacherous," as Professor Dewey 
thinks. There is no contradiction in its two uses — as a term of 
indefinite reference and as a term of discriminate reference. 
The part of the continuum which is out of sight and is, there- 
fore, not an object of thought is in the instrumental view, never- 
theless, always suggested by the present thinking. Now the dif- 
ference between the idealistic and the instrumental theory of 
judgment hinges upon the meaning of the word suggest. The 
instrumentalist says that this suggested aspect of the continuum 



b Experimental Logic, p. 10. 



THE MODERN INDICTMENT OF FORMAL LOGIC 15 

is never a part of the given; the idealist insists that the sug- 
gested fact is already in a profound sense a present fact, other- 
wise it would not be even suggested. Idealism provides, without 
contradiction, for both the discrete and the continuous aspect of 
the whole within which present thinking is set. Bradley and 
his followers, in making reality the ultimate subject in judg- 
ment have kept in mind these two uses of the word. 6 

Moreover, I can not think it wholly just to the traditional 
theories of knowledge to say with Professor Dewey that they 
were concerned entirely with the ' ' question of the eternal nature 
of thought and its eternal validity in relation to an eternal 
reality — that they were engaged, not with the genesis but with 
value, not with a historic cycle, but with absolute distinctions 
and relations." 7 The old pre-Darwinian metaphysics did not 
ignore the question of genesis, but it saw that all historical ques- 
tions are at last dependent upon questions of value, upon abso- 
lute distinctions. Even Plato recognized the fact that truth 
and falsity were organically related to practical life, to action, 
to the very needs in concrete experience upon which the logic 
of pragmatism lays such emphasis. And it is not attributing to 
Plato doctrines that are not his, to say, in the terminology of 
the new theory, that he did not teach that truth and falsity should 
be wholly divorced from the particular activities that we perform 
at a specific need. But he would reply to the pragmatists 
today in the spirit of his reply to the sophists, "The construc- 
tions of these specific activities are not true unless they conform 
not only to the intra-temporal is but to the supra-temporal 
aught." 

Professor Schiller asks the logician of the old school a simple 
question which he rightly says cannot be shirked: "When he 
asserts what seems to him a truth does he take any steps to ascer- 



sBosanquet says: "The subject in every judgment of Perception is 
some given spot or point in sensuous contact with the percipient self. But 
as all reality is continuous, the subject is not merely this given spot or 
point." Logic (ed. 2; Oxford, Clarendon Press, 1911), I, 78. 

7 Logical Theory, p. 14. 



L6 FOOTNOTES TO FORMAL LOGIC 

tain whether or not it is 'objective,' and whether other men 
(all or any) agree with himl H" lie docs, what arc they and 
what is their Logical valued Ii' he does not, why should not Ids 
claim be treated as a random one!" 8 But now this is precisely 
the question which a score of critics have been asking the prag- 
matist for the last two decades. In an essay on "Pragmatism 
and the a priori" printed in 1905, I said: 

A judgment must be more than B more effort to reconstruct the situa- 
tion in which we find ourselves from moment to moment; so much is, of 
course, the first condition it must fulfil. But in addition to being a suc- 

sful present response, it must be true. This requires that it not only 
conform to a passing is, but to a permanent ought. Each judgment of mine 
is, in one aspect, my response to a present situation. But before I am 
entitled to call it true, I must know why the response has been what it is; 
that is, I must be able to say that another than myself would have responded 
to the situation in precisely the same way. 

Experimental Logic tells ns that we must take all of our 
problems, logical, ethical, and even religious, to experience for 
solution. We must let the particular concrete facts of sense 
experience tell their story. But the result is, as I have tried to 
point out, experience has in the end no necessary story to tell. 
Did not Hume prove that once for all? If we follow the realist 
Ear enough, as he lets facts recite their tale of explanation, he 
invariably brings us back to the point from which he set out. 
Be displays a remarkable combination of true insight, with what 
seem inexcusable lapses from reason in his empirical explana- 
tions. These modern apostles of the "flowing philosophy," are 
standing upon a platform from under which all support has been 
taken. The pragmatist proceeds with his empirical test for truth 
paying no heed to the constant protest of the idealist against 
the circular reasoning that is involved in any attempt to make 
experience self-explanatory. To the idealist's question, How 
do yon explain the contradiction in experience? he replies 
naively, "There are no contradictions." Of course no contradic- 



■ Mind, ii. b. .Will (1909), 402. 



THE MODEEX INDICTMENT OF FORMAL LOGIC 17 

tion will ever be discovered in experience if he test experience 
by itself. 

The difference between the idealistic and the pragmatic inter- 
pretation of experience is to be found in the way in which each 
of the two schools reads off the relationship between external 
and internal meaning. For the idealist the whole problem of 
knowledge reduces itself to the question. How are primary or 
internal meanings of ideas related to their secondary or appar- 
ently external meanings? For the realist, the pragmatist, and 
in fact for every type of positivist, the question is, How are the 
brute facts of the primary objective reality related to the second- 
ary apparently internal meanings which we call ideas ? If experi- 
ence be taken in a wide sense as synonomous with the entire con- 
tent of consciousness, and thus made to cover both the active 
as well as the passive aspects of thought, then of course the 
idealist would agree with the empiricist that the laws of thought, 
as well as the laws of existence come from experience. 



Ill 

The critics of Formal Logic have failed, I venture to think, 
to distinguish between the thought form and the language form 
in which that thought form expresses itself. The two are not 
the same ; and Formal Logic deals with form in the first, not 
the second sense. Professor Sidgwick says, "Preoccupied as 
Logic has chosen to be with forms of statement, it cannot wholly 
desert the idea that the meaning of a statement is something that 
belongs to its form, instead of the form being a more or less 
successful attempt on the part of a speaker to express a mean- 
ing. ' ?! Not all teachers of Formal Logic, I am sure, would agree 
with this statement. The translation of the literary or rhetorical 
forms of statements into the logical form of thought, is the 
work of the grammarian and the philologist. We admit that the 



s Elementary Logic, p. 166. 



is FOOTNOTES TO FORMAL LOCK' 

grammat ical form is often highly ambiguous, and that it is a more 
or Less successful attempt on the part of the speaker to express 
a meaning — it is a thought form. But the thought forms are 
not ambiguous, although they have manifold meanings. It is 
the work of the formal logician to explicate the various impli- 
cations, or manifold meanings. 

It is a significant fact that in its indictment of the Tradi- 
tional Logic the New Logic does not condemn formal reasoning 
in toto. Sidjrxviek says: "We do occasionally reason about the 
extensive relation of two accepted classes to each other by means 
of the relation of each of them to a third class, and for that pur- 
pose we may put letters like X, Y, and Z, in place of the terms 
and so test the validity of a syllogism apart from the truth of 
its premises and conclusion." (Elementary Logic, p. 164). 
Now the defenders of Formal Logic may well regard this as a 
concession of the greatest importance. If there can be found 
a single instance where the form of thought does not have to wait 
upon the matter, controversy is at an end and the formal logicians 
have won the debate. This is all that Formal Logic has ever 
contended for, and we do not here avail ourselves of the prin- 
ciples that the exception proves the rule in the narrower sense 
of that axiom. These instances, where it is admitted that we 
reason formally, are abstractions from the concrete situations, 
and if the form can be divested of its matter in a single instance 
there is nothing to prevent our applying the principle univers- 
ally. 

Formal Logic, today, has set for itself the task of determining 
all indefinable concepts and all indemonstrable propositions. The 
several contributors to the volume on Logic in the Encyclopedia 
of Philosophical Sciences are quite in agreement on this point. 
We must bear in mind, however, that the modern process of 
Logical definition consists in pursuing a concept back to some 
prior indefinable concept. And we must always remark that, 
when we are dealing with a class of inter-related concepts, it is 



THE MODERN INDICTMENT OF FOEMAL LOGIC 19 

often immaterial which of the group are taken as the indefinable 
prerequisites of the others. In like manner the present-day 
Formal Logic regards the process of demonstration as the reduc- 
tion of all propositions to the least number of indemonstrable 
propositions. And here, too, in considering any collection of 
propositions constituting a real group it is immaterial to the 
structure of the group which is placed in the position of the 
indemonstrable proposition, and which are its derivatives. 10 



IV 

Of the four authors who in recent years have led the attack 
on Formal Logic, Dr. Mercier is the most vehement in his 
denunciations of the traditional system. He thinks it a serious 
indictment that among the foremost writers on the subject, since 
the time of Aristotle, no two are agreed on what the subject mat- 
ter is. what its limits are, or even whether it is a science or an 
art. He insists that it is neither logical nor useful to write upon 
a subject without first determining the nature of the subject 
matter. But this I think is not a serious indictment. Many 
investigators are doing most logical and most useful work in 
Dr. Mercier 's own special province of insanity, and yet we may 
say of these workers, as Dr. Mercier says of the formal logicians, 
that no two writers on the subject since the time of Pinel have 
agreed as to precisely who should be included in the class, insane. 

In his attack upon the Traditional Logic, Dr. Mercier has 
said that the system which he has propounded is so different 
from all previous expositions as to warrant the title, A New 
Logic, which he has given to his book. But in the opening pages 
of the volume we find him giving an account of the nature of the 
reasoning process almost identical with that which Aristotle gave 



10 Cf. Croce, Encyclopedia of Philosophical Sciences, I, 186. "It depends 
on us whether any particular axiom be taken as a theorem and any par- 
ticular theorem as an axiom, according to the order which Ave adopt in our 
deductions. * ' 



20 FOOTNOTS8 TO FORMAL LOGIC 

in the Prior Analytics. Dr. Mercier maintains that there are 
three processes of reasoning — induction, deduction and analogy. 
Now. however much Logicians through the centuries max- have 
differed from Aristotle in their own personal opinions of the 
nature of the reasoning process, they have all admitted thai we 
owe to him the tripartite division of the reasoning process into 
analogy, deduction and induction. Although Dr. Mercier lias 
condemned in very emphatic language the whole of Traditional 
Logic, yet when he comes to his own account of the three types of 
reasoning he says, when writing about deduction: "The Logic 
expounded in that book is the Logic of Inference ; of Consistency ; 
of Proof and Disproof; of Form. Useless in the discovery of 
Fact : ignoring the truth or falsity of the matter of which it 
treats; its value is in testing Consistency; in argument, in ex- 
plicating, convincing, refuting. This is the field of Traditional 
Logic/' 11 We thus observe that while denying the uselexsness of 
the Traditional Logic in the discovery of facts, Dr. Mercier 
nevertheless accords to it a w r ide field of usefulness in other 
directions. 

Dr. Mercier criticizes the logicians of the old school because 
they employ a nomenclature that is often inappropriate and 
ambiguous. He discovers, in the words describing the classifica- 
tion of propositions as real and verbal, a clear misnomer in the 
term, verbal; "for all propositions/' he says, "are expressed in 
words, and are therefore verbal. Here therefore at the very 
outset of our logical studies, we meet with a striking instance, 
the first of very many, of the inaccuracy, looseness, and ambigu- 
ity with which words, the material of their craft, are used by 
logicians." 12 But I submit that we should none of us write 
much upon the subject of Logic or upon any other subject, if 
we waited until words said exactly what they mean, or meant 
exactly what they said. It is interesting to observe, also, that 



w Logic, p. 11. 

"- Op. '-it., p. ] 7. 



THE MODEEX INDICTMENT OF FOEMAL LOGIC 21 

the classification which Dr. Mercier suggests, instead of the 
one ordinarily found in textbooks, is itself not free from ambigu- 
ity of the very kind which he criticises. We are all of us at the 
mercy of vocabulary. 

The idealists join the empiricists in deploring the imperfec- 
tion of language as a means of conveying thought about first 
principles. It is not a new discovery that language is inadequate 
to speculative thought. Nor does it require elaborate proof to 
show that language was created for the utilitarian purpose of 
communication in the world of appearances. The idealist, there- 
fore, describes his conceptions of final reality very unsatisfac- 
torily by means of a vocabulary which has had its origin in the 
world of relative reality. All who believe in the world of things 
that abide, must therefore express themselves imperfectly by 
myth, parable or metaphor. Plato, Christ and Buddha often 
deplored the defects of language in their attempt to teach the 
glad tidings of salvation through the sense of the universal. The 
scientist and the pragmatic thinker in general, who traffic in 
things seen, are not so handicapped by the short comings of 
language as are those who are concerned with the unseen. We 
make many allowances for the scientist when he expresses him- 
self in halting ways by means of our imperfect instrument of 
language, which does not keep pace, in its revisions, with the 
revisions of knowledge. We understand the astronomer when 
he says, ' ' Tomorrow when the sun rises I shall make some obser- 
vations. ' ' We do not rebuke him for the inaccuracy and expect 
him to say, "Tomorrow when the earth revolves and causes the 
sun to appear to rise, etc. ' ' The idealist bespeaks a like patience 
and tolerance from his hearers when he attempts to describe the 
still more distant realities by means of illustrations from the 
world of sense. He is fully aware that his metaphors are faulty, 
defective, and inconclusive. 



FOOTNOTES TO FORMAL LO<;ic 



V 



The genetic theory of judgment, upon which pragmatism rests 
its entire Logic, is stated most clearly and concisely by Mr. 

Schiller: 
I 
1 cannot but conceive the reason as being, like the rest of our equip- 
ment, a weapon in the Btruggle for existence, and a means of achieving 
adaptation. It must follow that the practical use, which has developed it, 
must have stumped Itself upon its inmost structure, even if it has not 
moulded it out of prerational instincts. In short, a reason which has not 
practical value for the purposes of life is a monstrosity, a morbid aberra- 
tion or failure of adaptation, which natural selection must sooner or later 
wipe away. 18 

In the present essay 1 wish to reaffirm the central criticism 
that idealism has made upon the logic of pragmatism ever since 
its birth — in its present reincarnation — in Professor James' lec- 
ture on "Philosophical Conception and Practical Results," be- 
fore the Philosophical Union of the University of California in 
1898. I shall attempt to show, as I have maintained elsewhere" 
that thought is not merely an instrument in the struggle for 
existence, not simply one of the devices with which nature lias 
equipped us to secure a more comfortable adaptation to our en- 
vironment. I shall contend that aside from being a useful instru- 
ment in the struggle for existence — its secondary and derived 
function — it has the more important primary office merely to be 
true. It has been asserted often in the history of Logic that 
thought has an external meaning, through which it refers to 
an end beyond itself, and an internal meaning which constitutes 
an end in itself. It is one function of judgment to be useful, 
that is. to reach out beyond itself. But its other and more funda- 
mental function — a function without which that other function 
is meaningless — is just to be true, to be self-consistent. 

Some pragma! ists have hestitated to commit themselves to the 
d net line that all judgments are practical. Such leaders, how- 



-■Humanism: "Philosophical essays (London, Macmillan, L903), p. 7. 
14 "Pragmatism and the " priori," Present series, I H904), pp. 72-91 



TILE MODEUX INDICTMENT OF FOBMAL LOGIC 23 

ever, as Schiller, Sidgwick and Mercier have unhesitatingly 
declared, not only, that all truth works, but also that all that 
works is true. But Professor Dewey seems always to leave his 
readers in doubt as to precisely what view he holds. In his very 
latest utterances he has again failed to make his position clear. 

In an article entitled, "An Alleged New Discovery in Logic" 
Mr. D. S. Robinson criticises Professor Dewey's Experimental 
Logic and remarks 15 that he is in doubt whether Professor Dewey 
would say that all judgments are practical. In his rejoinder 
Professor Dewey admits ' ; There is danger of a serious ambiguity 
in discussing practical judgments as a distinctive type and also 
intimating that in some sense all judgments may be practical." 
But when Professor Dewey "intimates" (not asserts), that 
"some" (not all) judgments "may be" (not are) practical, I, 
too, find myself in doubt. I am still old-fashioned enough in my 
idealistic convictions to think that the pragmatist can not avoid 
committing himself to at least one assertion that is not prac- 
tical — or at any rate not practical in the same sense as the 
others — namely, this very judgment that all judgments are prac- 
tical. And it is not mere quibbling to say that the judgment 
that all judgments are practical, is not itself a practical judg- 
ment. It is another way of saying that the judgments of utility 
are in one dimension of thought and the judgments that pro- 
nounce upon the members of the series of useful judgments are 
in a different dimension of thought. 

Empirical Logic 16 has always declared that all definition 
presupposes a psychological treatment of mental states; and 



is Jour, philos. and psych., XIV, 225, April 26, 1917. 

i« There is an important sense in which every theory of judgment is 
empirical. When I say that a judgment, or anything else, is empirical, 
one implication always is that it might have been otherwise. And in our 
theory that judgment is just such a selection from competing alternatives 
presented to the mind, this constitutes one of the earliest and most basic 
characteristics of the judging consciousness. Wherever we find the possi- 
bility of error, we are dealing with empirical facts. And there is this 
paradox about facts: to be real facts they must possess the inherent possi- 
bility of being different, and hence not facts. 



24 FOOTNOTES TO FORMAL LOGIC 

idealists have always admitted that a study of psychic facts as 
they are immediately presented to consciousness is indispensable 

to any doctrine of truth. But they insist that this is not the 
sufficient condition of truth; the apperceiving or unifying of 
the sense-presented facts is performed by the self-active prin- 
ciple of mind. If there is value to our individual experiences, as 
they come to us strung along in time, and if it is unnecessary 
to make this temporal validity rest back upon a validity that is 
not in time, all talk about a world of absolute truth and perfec- 
tion is meaningless. If Experimental Logic is self-sufficing, then 
there is no Logic ilberhaupt. 

Experimental Logic would explain my present thought by 
locating it between an a priori situation out of which it emerged 
and a subsequent situation into which it flows. Idealistic Logic 
maintains that the three situations — past, present and future — 
even when thus casually connected in the chronological series 
are not self-explanatory. There is exhibited in Instrumental 
Logic, we hold, the ancient fallacy of failure to distinguish 
between psychological cause and logical ground. 

The logical coherence in our judgments, according to Experi- 
mental Logic, is our interest in the situation in which we find 
ourselves, when called upon to judge. We are constrained to 
reconstruct that part of the world witli which we are in imme- 
diate contact. The union of the subject and predicate in judg- 
ment is the outer expression of this purpose or interest. This is 
certainly true as a psychological account of the judging process. 
But having said that interest or purpose is the cause of the inter- 
connection of ideas, we still have on our hands the more serious 
problem of finding the ground of the present purpose. This, 
as the idealist has often insisted, is not self-explanatory for cause 
and ground are not identical. It is one thing to say that we 
judge because we have a need, an interest, or a purpose; but an 
entirely different thing to discover the ground of this need. How 
may I know that this present purpose to reconstruct reality is a 



THE MODEBX INDICTMENT OF FOKMAL LOGIC 25 

true purpose ? Only when I have laid hold of a higher and ulti- 
mate purpose, namely, a criterion of this specific purpose. In 
short, I fail to see how purposes are capable of self-evaluation. 

Experimental Logic while emphasizing effects of action as 
tests of validity, does not furnish a criterion by means of which 
we may distinguish good from bad effects. Every judgment 
reconstructs reality, and thereby helps to continue the present 
order, say the defenders of the new theory of knowledge. We 
pronounce the judgment true if it contributes to the existing 
order, and false if it does not. But now, in order that we may 
distinguish a good effect from a bad one, we need some criterion 
extrinsic to the situation to tell us why it is best to have the 
present system perpetuated. In every experimental logic, truth 
means objectivity, and its criterion is utility. But in the prac- 
tical world there are different kinds of utility. If the useful is 
the true, we ought likewise to have grades of truth, and be able 
to speak of the true, the truer and the truest. This is, indeed, 
precisely what the pragmatist does say — a doctrine open to 
criticism, to say the least. Moreover, even if we admitted the 
possibility of gradations in truth (for the logic of realism insists 
that this is by no means manifestly absurd), the pragmatic test 
furnishes no criterion for distinguishing between the different 
kinds of truth. But it is evident that it is not mere utility, but 
utility of the right kind, that is needed to establish the objectivity 
in judgment. 17 

In every judgment, according to the pragmatic theory of 
knowledge, something new is added to the system of cognitions 
already in the possession of the one who judges. The test of 



«Cf. Windelband, Ency. Philos. Sci., I, 24. "And here we come 
on a double aspect of all logical laws: on the one hand they are rules for 
the empirical consciousness, according to which all thinking which has truth 
for its aim should be carried on ; on the other they have their inner and 
independent significance and being, quite independent of the actual hap- 
pening of ideational processes, which are or are not in accordance witli 
them. We may call the latter their value-in-themselves, the former their 
value-for-us. 



FOOTNOTES TO FORMAL LOGIC 

the rationality of this new elemenl is its compatibility with the 
old. [f it works it is pronounced true and is given its appropriate 
place in the established order. If it docs not fit in with the old 

i! is rejected as false. 1 > u t this definition of truth is more adroit 
than accurate. Is not the pragmafist all the while hogging the 
whole question .' Does he not presuppose the truth or rationality 
of the old. namely, this thought system which he possesses at 
the moment of judgment? His criterion of inner consistency 
works very well, if we grant him enough rationality to start the 
process. The instrumentalist, I should say, borrows just enough 
of the idealistic insight to set his scheme in motion and then dis- 
avows the debt. The idealist has ever insisted that this determin- 
ation of the primal rationality can never be achieved by a poste- 
riori methods. That which is workable is not, for that reason 
alone, true. A new fact may fit in with the old, and yet may 
not know itself to be error, because it does not know the system 
into which it has been accepted, is false. 

I cannot think that the total meaning of an idea is to be 
found by searching only forward from the idea to its conse- 
< l in ] ices, as Professor James teaches, nor yet by looking both 
forward and back as Professor Dewey and his disciples insist. 
The deepest truth about thought is found in an entirely different 
dimension. It lies in a w r orld that is logically prior to the postu- 
lates of either of these forms of pragmatism. Thought is con- 
structive as well as reconstructive. It is not merely an instru- 
ment in the struggle for existence, but is itself legislatively 
sovereign over the process of evolution within which it manifests 
its.lf as an instrument. Not what an idea has come out of, nor 
what it is just now seen to be, nor what it is going to do here- 
after, hut what it eternally is, must furnish us with our deepest 
insight into the nature of thought. 



THE MODERN INDICTMENT OF FOBMAL LOGIC 27 



VI 

The agnostic realism at the heart of every form of pragmatic 
logic is not easy to refute. It has descended directly from the 
agnosticism of the Critique of Pure Reason. The only way to 
dissolve this realism is to make use of Kant 's own discovery, and 
pursue his logic to the legitimate conclusion of its own movement. 
Kant pointed out the path that must be pursued in order to 
explain the inherent contradictions in the realistic conception 
of causality. He demonstrated, it would seem for all time, that 
the principle of efficient casuality cannot belong to reality, but 
that it is the mind's contribution to experience. However, he 
failed to see that for this very reason there can be no genuine 
datum in knowledge. If the facts of experience are really given, 
if they are thrown at the mind from the world of things in 
themselves — then this transcendent reality possesses the princi- 
ple of efficient causality. This, however, Kant's own doctrine 
explicitly denies. His insight enables us to see what he him- 
self seems never to have been fully aware of, that if the things- 
in-themselves have not in them the principle of efficient causality 
they are incapable of giving anything to mind. Things-in-them- 
selves can not contribute causally to the content of knowledge. 

The fundamental point at issue between Plato and Aristotle 
on the import of judgment has been perpetuated, in philosophical 
discussions, to the present day. The idealists say with Plato 
that necessary truth is that from which every purely material 
external or given element has been cancelled. The only truth is 
formal truth. The later-day pragmatic or instrumental logicians 
have insisted that truth as thus defined would be relegated to 
the world of mathematical abstraction, to the realm of ''bloodless 
categories. ' ' Plato provided for a more vital connection between 
the universal and the particular, the abstract and the concrete 
than appears on the surface. Aristotle's attack on Plato on 
this subject was not entirely defensible. And no serious idealism 



FOOTNOTES TO FORMAL LOGIC 

ai the presenl time imposes this requiremenl on knowledge. Plato 
did not demand thai the given, the concrete, the particular ele- 
ment in knowledge should vanish entirely. Now it is obviously 
a question as to the precise meaning of the given. The given 
may be so defined that it can be kept as a constituent element of 
the highest knowledge. A datum which is just hurled at a passive 
mind would, of course, contaminate knowledge and forever reduce 
it to relativity and incertitude. In perfect knowledge there can 
be no stn ng-gegi fa nes, nothing genuinely novel or totally differ- 
ent. But the logic of naive realism declares that such a Streng- 
gegi fa nes is an inexplicable and irreducible element of the know- 
ing process. Absolute knowledge, it declares, is forever impos- 
sible ; such opinions or beliefs as we have, we arrive at by a 
posteriori methods entirely. The logic of naive realism and the 
Instrumental Logic declare that we are not at all concerned with 
the ultimate beginning of thought. In fact, thought cannot be 
traced back to its source. It cannot see itself start ; it must 
simply accept itself as fact. But now it can be pointed out, even 
to the proverbial plain man on the street, that there can be no 
arriving at knowledge or anything else without starting. There 
must be a beginning somewhere, an initial point of departure 
which is itself underived. 

VII 

Empirical Logic has always dealt extensively with the word 
fact. All knowledge, it says, must have its foundation deep down 
in the world of concrete fact. To this we may reply: In order 
to reaUzi itself, thought must, to be sure, pass through fact. 
This Plato never denied, and the student in the philosophy of 
Kant learns, almost in his first lesson that the a priori forms of 
thoughl are empty and without meaning, until they have received 
their material filling. Thought does not see itself start. But we 
are not warranted in saying that because it does not see itself 
start, it arrives without starting. Of course, men reasoned acccu- 



THE MODERN INDICTMENT OF FORMAL LOGIC 29 

rately before they knew the reason for their accurate reasoning. 
They followed out premises to their conclusion, or traced con- 
clusions back to their grounds, guided by principles of correct 
thinking before those principles were noticed or understood. 
Aristotle was preceded by many centuries of exact thinking. It 
was not his primary purpose to make men rational — that, for 
the most part, they already were. He was interested to show 
men, by critical analysis, in what their existing rationality con- 
sisted. 

Thought does first become aware of its own movement as it 
passes through fact — as it issues out of one situation to go over 
into another. But this is not the last step in its self-realization. 
It is an unjustified arrest of thought's activity not to allow it 
to pass through fact and, returning to itself, to discover the 
underived laws of its movement. Thought does find itself by the 
way of fact, but when its activity is unhindered it passes to the 
higher level where it sees that itself furnishes the prior condition 
of the discovery of itself in the facts. To think actually, we must 
indeed think about something; this something, the object matter 
of thought, whatever it may be, must in the first instance be sup- 
plied through the medium of the senses. Thought itself does not 
become an object of thought until after it has been called into 
exercise by objects presented from without. But while the mate- 
rial or external element varies with every successive act of 
thought, the formal or internal element remains the same in all ; 
thus the necessary law, or form, binding on the thinker in every 
instance, is distinguished from the contingent objects, about 
which he thinks on this or that occasion. Obviously the words 
matt rial, external, and object are not here employed in any naive 
sense. In a later chapter, when we come to discuss more in 
detail the nature of the objective element in thought we shall 
define the object entirely in terms of the expected self-trans- 
cendence of the subject. 

The new pragmatic Logic and the modern realistic meta- 



FOOTNOTES TO FORMAL LOGIC 

physics underlying it — so their devotees frankly confess — 
acknowledge important contributions which they claim modern 
natural science makes to their doctrine. There has been a very 
prevalent tendency in the thinking of the last quarter of a cen- 
tury, to abandon or to ignore almost entirely what through all 
the aires has been considered the highest concern of the human 
mind, namely, the search for first principles, logically prior to the 
causal series and its validating ground in time and space. This 
tendency to abandon all attempts to orient our temporal experi- 
ences — our dynamic lives — by resting them back upon a static 
encircling reality is undoubtedly due to the enormous place that 
the method of natural science has come to occupy in the higher 
intellectual life of our time. The vast and comparatively sudden 
development in the biological sciences under the guidance of the 
master principle of evolution has filled many minds with an over- 
powering sense of the importance, the certainty and the useful- 
ness of this principle in other fields. But there are yet many 
unshaken idealists, 18 who still believe that Kant's first question, 
' * What can I know and how do I know it ? " has to be raised and 
answered, too, in a final and affirmative fashion, before the 
scientist has valid possession of his method even within the field 
where alone it is applicable. The validity of the scientific method, 
lies entirely in its application to its proper object, namely, the 
facts of sensible experience both inner and outer. But it does 
not follow that, because science can give no certitude in the real 
world beyond sense, there is no method of certainty possible in 
that super-sensible world. Metaphysics is absolutely indispens- 
able to the existence of Logic or of any other science. 

The theory of judgment that is offered in these pages demands 
an objective system which the judgment itself confesses must lie 
beyond its primary activity. But this postulated objectivity in 



i« E.g., Windelband Bays: "Modern Metaphysic, with its attempts to 
piece itself together out of borrowings from the sciences, is far more con- 
temptible than the old Ontology which, starting from the realm of validity, 
had at any rate the courage to attempt the deduction of the interconnection 
of the oniverse as an articulated whole." Ency. Philos. 8ci., I, 65. 



THE MODE EX INDICTMENT OF FORMAL LOGIC 31 

judgment, as I shall try to show later, is not inconsistent with a 
monistic theory of the universe ; it is even compatible with the 
most naive subjective idealism. However, it provides for a relax- 
ing of a too-rigid monistic ontology. When we declare that the 
subject awaits its object, and then define that object as no other 
than this expected self-transcending, synthetic achievement of 
the subject, we avoid the contradictions of an epistemological 
dualism on the one hand, and an ontological monism on the other. 
Both for knowledge and for existence the idea and its object 
are — to use Bradley's very apt expression — "coupled apart." 

The New Logic is distinguished from all the older idealistic 
systems by its refusal to accept the distinction between ground 
in fact and ground in thought. As has now frequently been 
pointed out, pragmatic Logic dispenses entirely with ontology in 
the historic sense of the word, and therefore, identifies the cause 
of the existence of serial facts — in their serial manifestation — 
and the ground of our thinking them serially. We hold that this 
distinction is vital and that, while there is a practical viewpoint 
from which it may be ignored, it cannot be totally cancelled. This 
is one of the first and most persistent criticisms that various 
idealists have made upon the instrumental theory of judgment. 

The genetic theories of judgment are all compelled to admit 
that the ground of belief is finally an unsolved problem. Psy- 
chology seems to have discovered that chronologically we believe 
things first and afterwards demonstrate them. Thinking as dis- 
tinguished from believing is retrospective rather than prospec- 
tive : it is demonstration rather than inference. Now it is not 
only Psychology that confesses itself baffled with this puzzling 
question of the reason for our beliefs, but Logic also finds the 
ground of knowledge in a sense inexplicable. As I have already 
said, knowledge is a postulate of logic ; it is a fact that must be 
assumed before logic itself can come into existence. If Logic 
is "thinking about thought," then this thought is obviously taken 
for granted when the thinking about it begins. 



FOOTNOTES TO FOBMAL LOGIC 

Professor Dewey has often admitted,' 1 ' by implication at any 
rate, that he lias not remained true to the Hegelian idealism of 
his earlier writings. And yel many of Ids later utterances seem 
to me as entirely opposed to the naive associationism of the earlier 
empiricists, Locke, Mill, and Bain, as is any idealism. And there 
are also serious divergencies from the even more radical empi- 
ricism of the Later pragmatists, Schiller, Sedgwick and Mercier. 
For Professor Dewey's ideas taken by themselves are entirely dis- 
crete facts. They are continuous only when embedded in the 
specific situation out of which they arise and into which they 
descend. And yet I must repeat that I fail to see how the "situa- 
tion" with all its "brute" objectivity can ever provide for the 
continuity that is necessary for "knowing things together." 

I wish to offer a homely illustration of an illusion of continuity 
in the optical world analogous to the essential discontinuity that 
lurks in the instrumental theory of thought. Each of the various 
moments of a motion picture as they are flashed on the screen 
might be described in terms of what precedes and what follows 
it. We say we watch the scene being enacted, we follow the plot 
and we think we see explanatory continuity there. But if an 
imaginary being, living in that screen world — totally unaware of 
the projecting power of the stereopticon — were asked to give an 
account of what really does happen, he would say precisely what 
Hume said about the world that we actually see. No causal con- 
tinuity is found on the screen. One picture appears and then 
disappears and another totally disconnected from the preceding 
one takes its place. The clever makers of the motion pictures, 
taking advantage of actual discontinuity, can feign all kinds of 
continuity by piecing together parts of films taken miles and 
days a pari. The only truly explanatory continuity is found when 



!. Studies in Logical Theory, p. 36. "There is do such thing as either 
coincidence or coherence in terms of the elements or meanings contained in 
any couple or pair of ideas taken by Itself. It is only when they are co-factors 

in a Situation or function which includes more than either the ''coincident'' 
Or tie- "coherent" and more than the arithmetical sum of the two, that 

thought's activity can be evoked." 



THE MODE EX INDICTMENT OE FORMAL LOGIC 33 

we read our way back at each instant to and through the project- 
ing power of the stereopticon itself. So, too, must the states of 
consciousness that appear chronologically in the instrumental 
theory of judgment be translated into a thought process that 
transcends time and of which that outer evolution is but the 
projection. 

A less concrete, and therefore in some ways a more satisfac- 
tory illustration may be taken from geometry to show the essen- 
tial discontinuity in the stream of consciousness. The points of 
a parabola, for example, take their places seriatim in obedience 
to the requirements of facts external to themselves. Each point 
obeys the law of keeping equidistant from a fixed straight line 
and a fixed point ; as a particular fact in the series, it is inde- 
pendent of the points that lie next to it. An external spectator 
might imagine that the points arranged themselves in this orderly 
fashion by a kind of reciprocal reference to each other. Each 
point, it might be thought, could find its place in the series by 
taking its bearings from its predecessor and passing the angular 
reading on to its successor. But the curve has no such intrinsic 
principle for its spatial determination ; it is the result of the indi- 
vidual compliance of each point with entirely external conditions. 
The straight line, however, can and does define itself as a quantity 
in extension by precisely such an intrinsic principle. One has a 
practical illustration of this in watching a company of soldiers 
"fall into line." 



CHAPTER II 

APPREHENSION, QUESTION AND ASSERTION 

I 

It has frequently been maintained that Logic is not concerned 
with the question as to the structure of the idea, or how many 
ideas may be grasped in a single pulsation of consciousness, or 
any other of the many questions in which one idea is involved. 
The unit of Logic, we are told, is the judgment, and every judg- 
ment contains at least two ideas. Bradley and his disciples have 
rightly rejected the view that judgment is the comparison of two 
ideas. However, there is a sense in which we may say that two 
ideas are involved in every judgment. The ultimate molecule of 
knowledge, to use a chemical metaphor, is always diatomic. Con- 
scious judgment is the idea that I have an idea. To have, or to 
entertain an idea is to refer it to reality ; but this reference of the 
idea to reality implies at least one other idea which might have 
been referred to reality instead. If we had only one idea we 
should never, I think, distinguish between it and reality and we 
should never talk of referring it to reality. 

Obviously, these questions which lie in the borderland of 
controversy between Logic and Psychology can never be settled 
until we know precisely what we are to understand by one idea. 
It' we mean by an idea a state of consciousness so immediate and 
withal so simple and single in its structure as to exclude all 
internal multiplicity, then Logic can have nothing to do with 
it. and perhaps not Psychology, since the existence of a mental 
state described by Jevons and the earlier logicians and psycholo- 
gists as simple apprehension, lias justly been called in question. 
That may always he regarded as one idea which includes within 

[ 34 | 



APPBEHEN SION, Q UESTION A X D . I S S EB TIOX 35 

its synthetic grasp all the secondary ideas which a purposive will 
cares to make in it. It is the purpose to hold the multiplicity as 
a single object of attention that makes it one idea. The only true 
individual is a will-object. From the point of view of the act of 
synthetic attention the idea is one, but it is not on that account 
simple. For this reason the expression simple apprehension is 
a misnomer. Apprehension may be of multiple content. For the 
purpose of the present discussion we need not go further into this 
controversy. 

It should be pointed out, however, that the expressions, mental 
states, state of consciousness, idea, image, are all of them ambig- 
uous, and this ambiguity when carried over into the logical debate 
becomes the source of hopeless confusion, and the " cause of all 
our woes. ' ' Xo word in Logic has caused more confusion than the 
word idea. Even in ordinary usage it has been taken to stand 
for both a universal and a particular content of consciousness. It 
would be better to regard the idea as one aspect of the concept. 
My concept of a tree may be analyzed into three moments: (1) 
the existence of an image in the mind which might be called my 
idea, of the tree, (2) the aggregate of inner qualities, (3) the ex- 
ternal reference or significance. Bradley, as is well known has 
characterized these three moments as (1) the that, (2) the what, 
and (3) the meaning of the idea. Logicians and psychologists still 
use the word ielea instead of concept, which is freer from ambig- 
uity. The concept is not exhaustively understood when it is 
treated psychologically only ; it is more than just a simple psychic 
act. The word idea in its more limited use does stand for such a 
focus of analytic attention. But no idea is mere idea ; the cogni- 
tive function, that is, the relation to something beyond itself, 
which it means, is necessary to the very being of the idea. And 
yet, self-contradictory as it may appear, we must say that when 
we have an idea of an object that object is already an essential 
part of the idea. For Logic, the idea, or mental state is a one 
enwrapping a mam). It is a content contemplated from a mul- 



36 FOOTNOTES TO FORMAL LOGIC 

tiple, that is. a dual viewpoint. Prom one of these points of view 
the idea or concept is a plurality; in its outward relation to the 
real of the universe it is many. But when it faces the thinker, it 
is one: its former plurality has now become the object of a single 
aet of attention. 

Some psychologists have analyzed thought out into a serial 
arrangement of its acts in which we find the concept placed 
between the judgment ami abstraction. The judgment depends 
upon the concept and the concept in turn depends upon the pro- 
cess of abstraction. No serious objection can be made to this 
serial arrangement if we do not construe the relationship of 
dependence as a uni-directional function. The structure of the 
concept and the judgment are different only for Psychology, for 
Logic they are identical. When I say the sky is blue there is pre- 
cisely the same thought of the relation in the act involved as when 
I say the blue sky. The difference lies in the fact that the concept 
is pure receptivity while the judgment meets the datum with a 
reaction in the form of an acceptance or a rejection. 1 The judg- 
ment discovers the concept as an isolated state of consciousness, 
atrophied or bereft of the support of reason. It rehabilitates it 
by connecting it again with its reasons. There is, therefore, 
partial justification for regarding the concept as prior to the 
judgment. But on the other hand the concept in the first instance 
was constituted by an act of judgment or abstraction, and so 
there is truth in the remark that judgment both precedes and 
follows the concept. Again we must observe here the distinction 
between idea and concept. The idea is always particular; it is 
composed of sensuous elements and is static. The concept is uni- 



1 Oroce seems to discredit unduly Buch an analysis of the content of 
consciousness. Be remarks: "This division concept, judgment and con- 
clusion involves the assumption that three different moments can be dis- 
tinguished within what is really a single and unanalysable act of thought. 
As B matter of fact, no one will ever succeed in thinking a concept, a real 
concept or B judgment which is not at the same time a conclusion, being 
Connected in B system with other conceptions and judgments." It is 
doubtless true as Uroee says that no one will ever think a concept by itself, 
but it Lfl not impossible to think the concept in its coordinated position 
within the whole of a specific content. Ency. Philos. Sri., I, 202. 



APPREHENSION, QUESTION AND ASSERTION 37 

versa! ; it is the power or capacity of a perception to mean some- 
thing — to stand for something external to itself. The idea is the 
psychical image that comes and goes. The concept is the signi- 
fication or the fixed content. 

Berkeley and the other nominalists were plainly right in their 
criticism of Locke's doctrine of abstract ideas. Locke described 
the process of abstraction as an affirmative act of mind. Thought, 
on this view, selected the common characteristics in several 
objects, and tied them up in a separate bundle with an existence 
and meaning of its own. But it is more accurate to speak of 
abstraction as the result of negative thought. The abstract or 
general we get, not by attending to what is like in several objects, 
but in neglecting what is unlike. A great deal of the difficulty 
that hangs about this subject would be removed if we observed 
the distinction between having and possessing an idea. It is one 
thing merely to have an idea and quite a different thing to have 
it as your own — to possess it — that is, to have it in relation to 
other ideas. It is the old familiar distinction between cognition 
and recognition. 

II 

The object of description must be an object in relation. Unre- 
lated objects are, as Hegel rightly said, indescribable ; they can- 
not even be named. The attributes in terms of which I describe 
any object immediately presented to consciousness, are all of them 
expressions of the relations of the presented object to objects not 
now present — that are elsewhere in space and time. Descriptive 
judgment must, therefore, always be conceptual or representa- 
tive. If there were only one object in existence we should not 
need a name for it, although we might need a word to distinguish 
between the existence and the non-existence of this single object. 
Naming is an act that belongs to the world of exposition and com- 
munication. We attach labels or names to objects only for the 
purpose of distinguishing them from other objects. 



FOOTNOTES TO FORMAL LOGIC 

Bui prior to our knowledge of the objed as described, we 

know the object as merely apprehended. There is, to be sure, 
serious objection to Baying thai we know the object in this first 
simple awan ness. The word know is full of all sorts of ambigui- 
ties and it is one of the purposes of these studies to isolate some 
of its meanings. When we say that we know the object, in both 
common and technical usage, we mean that we are not only aware 
of it. but that we arc aware of it in its describable relations. 
Knowing is a relating activity. But it is quite impossible to find 
a word that will perform any less ambiguously the self-contra- 
dict ory task of connoting the absence of connotation. However, 
there can be no doubt about the fact. 

The expression, immediate consciousness which is often em- 
ployed to describe this primitive datum of knowledge, stands for 
a mental state that is already well along toward the stage of 
description by means of relations. The word consciousness itself, 
etymologically at any rate, connotes a togetherness. But it is 
very important to distinguish between internal and external 
relatedness. We shall insist that this first direct awareness brings 
to us knowledge of isolated concrete wholes, within which we see, 
or appreciate, or know qualities in relation. 

It must be repeatedly emphasized that the state of mind that 
has now so often in Logic and Psychology been called simple 
apprehension is one of just pure acceptance or acknowledgment. 
It is a psychic experience in which there is no distinction between 
our apprehending the object and the object which is apprehended. 
Psychologists and logicians have been pretty much of one mind on 
this point, but there has been little agreement upon a word to set 
forth the mental state itself. Hobhouse has described the general 
characteristics of immediate consciousness of a fact by the word 
assertion; this has somewhat released the fact so known from 
being related to other facts. But the word assertion has now too 
often been employed as a synonym for affirmation to warrant 
its being transferred to this primitive awareness or pure recep- 



APPREHENSION, QUESTION AND ASSERTION 39 

tivity. And doubtless the same objection could be made to the 
term acceptance; the latter, however, is freer from the notion of 
activity, or decision. The expression "assertion of the object " 
already suggests that thought has gone out to meet the object 
with question, criticism, and decision. I think the word acknowl- 
edge is the most satisfactory for this primitive state of conscious- 
ness. In letter writing we distinguish between acknowledging and 
answering a letter. So when the mind receives its facts it may 
just acknowledge them, it need not go further and reply to them. 2 

Every fact is, indeed, related to other facts in the real world, 
but I need not know this in order to proclaim my acceptance of 
one of the related facts as an isolated thing. I can take it at its 
face value : I can bow my acceptance or acknowledgment of it. 
When I merely contemplate the red rose, that is, when I appre- 
hend it simply. I acknowledge something immediately present, 
and nothing more. I am aware of the red color, but am not aware 
of the relation of the red color to anything else. When I say, the 
tree in my garden is tall, I am undoubtedly describing the object 
by means of its relation to other objects. I am also quite truly, 
although not so obviously, describing the tree through its rela- 
tions when I say the tree is green. But such description is sub- 
sequent to mere apprehension, and is always in the interest of 
communication. The descriptive judgment functions socially. 

The apprehended content cannot contain the relation of the 
object apprehended to any other object. It merely envisages its 
own system of inner relations. In looking at a net from a dis- 
tance. I can be aware of the knots without thinking of the threads 
that run from knot to knot. I can gaze at the star, Sirius, con- 
template, accept, acknowledge it without consciously relating it 
to other stars. But as soon as I wish to describe — that is, com- 



- The critical analysis of the thinking process had revealed even to the 
Greek logicians the two factors of apprehension and assertion in every 
judgment. They distinguish clearly between Kard0e<m and ovyKaTadeats. 
These two aspects of the judging consciousness are also recognized, it seems 
to me, in the distinction between artheilen and beurtheilen, which several 
modern writers have proposed. 



LO FOOTNOTES TO FORMAL LOGIC 

mnnicate to my fellows — what I have thus apprehended, I must 
betake myself to the discovery of the relation of Sirius to other 
heavenly bodies. Every description of an object, of course, pro- 
ceeds always by means of relations; but the object so described 
was undoubtedly already present as an unrelated fact. It was 
once merely acknowledged. To accept or acknowledge the fact 
is one thing, to describe it another. 

Now it is not until we arrive at the stage of description that 
we may properly speak of the psychical process as judgment. The 
mental state which I have here called acceptance, or acknowledg- 
ment, has often been described as inchoate judgment, or sensory 
judgment. There can be no serious objection to such an account 
of this primitive stage of acknowledgment provided we keep in 
mind the real difference between it and true judgment. At the 
second stage we have the possibility of error. In simple appre- 
hension, or acknowledgment, there is no question of truth or 
falsity, and hence no possibility of error. The object presents 
itself and we accept it without comment. Moreover, the object 
of an unquestioned simple apprehension — an acknowledgment 
without comment — is always unalloyed fact, that is, fact present 
and unembarrassed by attachment to any fact not present. We 
can make no mistake in such an acknowledgment or acceptance. 
It is only when we comment upon the acknowledged fact, when 
we venture out along the relations of the present fact to other 
facts not now present that error arises. But then we are no longer 
merely apprehending the object we are making a judgment about 
it. We must distinguish therefore between assertion without 
comment or risk, that is, just acceptance or acknowledgment, and 
assertion with the risk that accompanies the necessity of selecting 
from competing alternatives. The latter is true decision, it is 



I cannot therefore agree entirely with Bosanquet that "being dis- 
tinctly aware of reality is another name for judgment/' (Essentials of 

Logic, ]'. M) . It' we should make use of the well known distinction between 

clear and distinct knowledge, of Descartes ami Leibnitz, in which distinct- 
points Inward and clearness outward, we might say that being clearly 
aware of reality is another name for judgment, and being distinctly aware 
of reality is another name for the simple apprehension as 1 view it. 



APPREHENSION, QUESTION AND ASSERTION 41 

affirmation or denial. As Hegel has said, to assert that a carriage 
is passing the house is not a judgment unless we are in doubt 
whether it is a carriage or a cart. 

It has been doubted, and with reason, whether we can ever 
entertain a significant simple apprehension without decision. It 
must be admitted, that as occurrences in a continuous psycho- 
logical process, apprehension of fact and decision concerning it 
are inseparably connected. They are, nevertheless, logically dis- 
tinguishable. In our normal adult life any longitudinal section 
of consciousness would reveal a highly complex mental state. We 
should never find in such cross-sections of the stream of conscious- 
ness, at first apprehension and then judgment. Both would 
appear in each and every cross-section. And we can take thought 
about any one of the elements in the complex content only by 
abstracting from the real organic process itself. The two acts, 
apprehension and judgment, though theoretically separable are 
joined in one concrete state of consciousness. We do not first 
find apprehension, and then decision and then action. All normal 
waking consciousness is one continuous affirmation, and, within 
this persistent judgment, simple apprehension is seen to be a 
distinguishable, though not a separate element. Moreover, it 
must not be supposed that the two aspects, apprehension and 
judgment, merge by imperceptible gradations one into the other. 
We have already seen the true differentia. Simple apprehension 
is naive in its attitude toward the apprehended fact, judgment 
comes with the discovery that the observed fact might have been 
different. 

Midway between immediate awareness — the primary datum 
of knowledge — and the full-blown judgment, there is found the 
impersonal judgment. This type of judgment has caused much 
trouble, but only to those logicians who set up arbitrary and 
impassable barriers between the different compartments of mind. 
There is no especial difficulty in understanding the impersonal 
on the view that regards all waking consciousness as an organic 



»- FOOTNOTES TO FORMAL LOGIC 

whole and that thinks of the concept, the judgmenl and the 
syllogism as the varying degrees of explicitness in which this 
whole expresses itself. Much of the controversy in the history 
o( Logic about Lmpersonals would have been entirely removed 
if the distinction between the judgment and the proposition had 
always been distinctly recognized. 1 

Now there can be little objection to the assumption — and 
obviously it must forever be an assumption — that the earliest 
states of consciousness in the development of the individual mind, 
are of this undifferentiated character. In childhood, and per- 
haps in the animal consciousness, we find simple awareness the 
sole content. There is more difficulty in the view that we may 
again relapse into this level of simple awareness, from our later 
normal adult consciousness, in which we are cognizant of the 
distinction between subject and object, the self and the non-self. 
Bradley is certain that, both prior to and subsequent to the stage 
of consciousness in which there is a distinction between subject 
and object, there is a stage in which we are not thus aware of 
the distinction between what is known and the knower thereof. 
We are quite justified, it would seem, in our inference as to 
animal intelligence from our own human experience of the stream 
of ideas, or reverie. 

It is in one sense wrong to call simple apprehension the 
primary operation of the mind. In describing simple apprehen- 
sion as the primary datum of knowledge I have pointed out that 
the terms, earlier and later, are out of place in any account of 
the relation of judgment to simple apprehension. Every imme- 
diate apprehension is simultaneous with a judgment and every 
judgmenl with an apprehension. 

There is a point of importance that must now be noted. We 



« I think, for example, that Couturat, who is otherwise very mindful 
of this distinction, has ignored its importance in his discussion of the 
impersonal proposition. He says: " /I rains is an indeterminate and incom- 
plete judgment. This example shows us at the same time that there are 

judgments without terms, without subject or attribute." Ency. PMI08. 8cL, 

I. 1:;!'. 



APPPEHEXS10X. Q UES TIOX A X D A SSEB TIOX 43 

have seen how judgment transcends simple apprehension by 
inquiring into the outer fortunes of the apprehended fact and 
discovering its external relations. As merely apprehended the 
fact was unequivocal; it was an immediate feeling, a knowing 
and being in one. But now the discovery of the relations of the 
apprehended fact to its fellow facts in the objective order is the 
discovery, also, that each of these relations might have been 
different. Thought has thus transcended the unambiguous simple 
acknowledgment of fact. But in passing to this higher stage of 
decision, or judgment, that is, the stage of selection from among 
possible relations, the original simple apprehension does not dis- 
appear ; it remains continuously in view as the foundation of the 
later selective knowledge. Immediate awareness is not a stage 
that appears and then disappears. 

Ill 

It will not be out of place to pursue this analysis a step 
further. Can we not discover a stage in the complex content of 
consciousness prior to apprehension? Do we not first have the 
fact in the experience of one moment and then in a subsequent 
moment apprehend it? Such a distinction has been made. It 
has been held that to be in consciousness and to be apprehended 
are not identical stages, that mere presence in consciousness 
does not imply even in the faintest degree the subject-object 
relation, while in apprehension the relation of consciousness to 
the presented fact has for the first time become explicit. But, 
in my opinion, this is a refinement of distinction that cannot be 
defended. To be in consciousness and to be apprehended as being 
in consciousness are identical facts, and both postulate the sub- 
ject-object relation. The content of simple apprehension is non- 
relational but this does not exclude internal variety in the 
content itself. This immediate awareness unrelated in itself 
but yet embosoming distinctions is, I believe, what Bradley has 
continually spoken of as " feeling. ' ' 



h FOOTNOTES TO FORMAL LOGIC 

It has been urged as an objection to every such analysis of 
the Logical contenl of consciousness thai it hopelessly confuses the 
psychological with the Logical point of view. Logic, it is said, 
demands real distinctions — definite lines of demarcation. Hut 
1 sec no reason for contending that logical consciousness is any 
more definite in its entire content than is psychological conscious- 
ness. We do not go wide of the mark when we say that the 
Logical apprehensions, like the psychological sensations shade by 
imperceptible gradations from explicit to implicit and vice versa. 
The content of sensation has its focal point of greatest clearness 
from which it fades away to a zero point of indefinitness ; also, 
we apprehend, or comprehend, or know by means of the concept, 
the judgment, or the syllogism in varying degrees of explicitness 
of the content. 

We must insist again that this immediate experience does 
not represent a stage in the psychical development which is at 
one time present and necessary and later disappears. When the 
discrimination between the self and the non-self has arisen and 
we find the relational type of consciousness, this primary aware- 
ness must still be a felt aspect of the whole content. As Bradley 
has said, "all that is thus removed is the mereness of immediacy.'" 
The one point which I wish to repeat with especial emphasis is 
that it is an error to suppose that our conscious contact with 
the world of objects starts with judgment. Reality has been 
presented to mind in its first simple awareness — the object has 
been accepted as a constituent datum of knowledge. The expres- 
sion "a mere suggestion" hints at this stage of simple appre- 
hension where fact has been accepted without affirming it. 

It would, perhaps, be a more precise account of the primitive 
datum of knowledge to call it an inner movement of analytic 
attention confined entirely to an immediately presented fact. 
But we should guard against the mistake of thinking that in 
this earliest stage of consciousness any act of classification is 
involved, for this would imply a comparison with other facts not 



APPBEHENSION, QUESTION AND ASSERTION 45 

now present. We must also distinguish between the judgment 
to which we have passed in proceeding outwardly to a classifica- 
tion of the given fact with other not-given facts, and the ground 
of this judgment. Theoretically at least, we may say that the 
ground varies from the zero point of complete indifference, or 
unmotived assertion, to complete conviction, or internal self- 
sufficing satisfaction. But now, this stage of apprehension, which 
Ave are attempting to fix, is at a level below the zero of sheer 
doubt. The doubt is always a decision not to decide. Apprehen- 
sion, however, has not even this characteristic, for here we have 
just the self-revelation of the inner content of the datum, and 
about that there is no doubt. 

It will be seen that this account of the relation between appre- 
hension and judgment is in close agreement with Wundt 's theorj^ 
that all judgment in the last analysis involves an act of will. 
Professor Adamson has challenged this view, asserting that judg- 
ment requires no reference to reality beyond the ' ' sensible press- 
ure," that it is just the belief in the existence of the objects 
from which the sense perception issues. Judgment, he says, 
' ' requires in addition to the belief that 'something exists, no con- 
sideration as to Avhether the belief itself be true." This, I think, 
is a doctrine that is opposed to fact. In our account every judg- 
ment calls for a decision as to the validity of the fact. In this 
state of consciousness that Professor Adamson has described as 
already the beginning of judgment, we have only analytic atten- 
tion to the pressure from the sense-presented fact, not analytic 
judgment. 



CHAPTER III 

THE IMPORT OP JUDGMENT 

I 

The various questions about the nature of judgment — the 
relation of subject to predicate, of percept to concept, of analysis 
to synthesis, of form to matter — all presuppose that the word is 
has one well-defined meaning. But the problem of the copula is 
besel with world-old difficulties. Russell, who is always tem- 
perate in his statements, has said, "Is is terribly ambiguous," 1 
and has pointed out five quite different meanings. And 
DeMorgan before him, with his eagle's eye for paradoxes and 
ambiguities remarked : ' ' The complete attempt to deal with the 
term is would give the grand cyclopedia, and its yearly supple- 
ment would be the history of the human race for the time." 2 

It will not be necessary for our present purpose to go far into 
the subtleties of these modern discussions of the meanings of is. 
It should be pointed out, however, that these ambiguities are not 
new discoveries. Aristotle was fully aware of the unavoidable 
ambiguity in any word that is made to serve as connecting link 
between subject and predicate in judgment. Following his 
teacher, he spoke most often of the relation between the world 
of concrete things and the world of ideas, which is expressed in 
the judgment, as one of participation. And for twenty-three 
e<nt uiies. from Aristotle to Bradley, the expression "participate 
in" lias been condemned for its metaphorical vagueness and 
ambiguity. The important thing to be borne in mind is that at 
heart it is always the same relation, whether we say that a thing 



i Principles of Mathematics (Cambridge, University Press, 1903), I, p. 64. 

-Formal Logic (London, Taylor, 1847), p. 49. 

[46] 



THE IMP OH T OF jmG M E NT 47 

is a copy of the idea, or that it participates in it, or that it is 
the idea. And the essential characteristic of this relation 
between subject and predicate in judgment is that it is non- 
temporal. This fact, namely, that the relation is not in time, 
while the relata are, will receive fuller elucidation in the sequel. 
It is for the reason that the time element is both in and around 
the judgment that some part of the verb to be has always been 
preferred to express the relation between subject and predicate. 
As has so often been pointed out, if there were no reason why 
the verb to be should be used as the sign of predication it would 
be difficult to explain its presence in so many languages. 

Among the many meanings of is, its existential import should, 
of course, be considered first. The copula in the proposition, 
S is P, in the first instance, stands for the fact that in every 
judgment there is undeniably present to consciousness a some- 
thing. However widely they may differ in other ways all theories 
of predication are agreed upon this point. We are not now inter- 
ested in the question whether this affirmation of presence is of 
something present to consciousness or in consciousness, that is, 
whether it is to be regarded as a datum or ideatum. The "pre- 
sence" characteristic of is must be taken as original — it is not 
derived from or constituted out of relations between the presented 
object itself and another object. It has no temporal origin. The 
present which is asserted in the judgment is not a somewhat 
coming after a priori past. Nor is it to be defined as the imagin- 
ary line of demarcation between the past and the future. The 
present is not that which comes after something past, but the 
past is something which came before the present. Is stands 
always as the reminder that knowledge is won by the extension 
of the present. 

It is no disparagement of the underived validity of the present 
to show, as may be shown, that we have not achieved knowledge 
until we have thus expanded the present into its relation with 
things other than itself. If thought were confined strictly to 



FOOTNOTES TO FORMAL LOGIC 

tlic present it would not know it, and we should never be impelled 
to judge. In judgment the present yields to the internal con- 
straint to transcend itself. Bui the apprehension of the present 
and the effort, in judgment, to pass beyond the present must 
not be confused. They are different acts. The present as imme- 
diately apprehended is singular — it is a this unrelated to any 
that. Bu1 as a this it is the unification of its own unique attri- 
butes; as apprehended fact it owes no allegiance to its other. 
But knowledgi of this as distinguished from its apprehension 
docs require an insight into the relations of the this to the that. 
The system of Hegel differs from other idealistic philosophies 
on the question of the time factor in judgment. Hegel disci-edits 
immediate consciousness, declaring that the conception of immed- 
iacy breaks down under the strain of its own inherent self- 
contradiction. I can apprehend an object presented to conscious- 
ness in one act and in a second act of thought I can be aware of 
the first state, but not as immediately present. I cannot think 
that I think, I can only think that I thought. But this does not 
seem to me to be a valid objection to immediacy of consciousness. 
It is true that we can never communicate descriptively the present 
state of consciousness without judging and thereby causing the 
present to slip away from itself into the past. The second act, 
indeed, is not immediate in the same sense as the first act. When 
I say "I think that I thought," the "I thought" which is the 
object of "I think" is. indeed, other than that which thinks it, 
but otherness is here unjustifiably construed as equivalent to 
past. The Hegelian recourse to memory is unnecessary. Intro- 
spection, I think, will also discover that memory plays no such 
part, as Hegel thought. When we examine the thought that has 
this possession of an immediate content, we do not find in it any 
act of remembering, as this doctrine declares. The mind seems 
truly to be noting something which is present to it then and 
there. "What I feel" says Bradley, "that surely I may still 
feel though I also at the same time make it into an object before 



THE IMPORT OF JUDGM EN T 49 

me. ' ' None of the various words that are compounded with self — ■ 
self-consciousness, self-contemplation, self-reproach, etc. — sug- 
gests a combination of the present with remembered aspects of 
itself. Subject and object are both in the same present time. 
This is illustrated in the humorous poem the first line of which 
runs "Says I to myself, says I." 

It is true that the complex content of immediate consciousness 
may experience one aspect of itself to be more vividly present 
than another. But these remote or less vivid aspects are not 
therefore to be relegated to the past. Differences in the "felt 
immediacy" are like the differences in the marginal vision of the 
eye. They are all present in varying degrees of definiteness. 
I can not, obviously turn the whole content of consciousness into 
an object at once. A part of the self must be held in reserve, 
so to speak, to be the experiencing subject of the part that has 
taken its place as object to be experienced. And the line of 
cleavage within the whole content may differ for different pur- 
poses. Also the sameness of the parts does not exclude differ- 
ences. In the line ' - Says I to myself, says 1, 7 ' the person speak- 
ing and the person addressed are the same and yet obviously 
different, for the better self is addressing the evil self. 

It is important in discussing the meaning of is to distinguish 
between being a.nd existence. Every conceivable thing, every 
object of thought has its being, but not all have existence. The 
minimum requisite of being is the quality of number. Anything 
that can be thought of as having membership in the number 
series has the quality of being.. But things have existence only 
if they "stand out" in systems of special inter-relationship. We 
may deny the existence of anything only if we are able to save 
its being. Contradictory as it may seem we must say that what 
does not exist must still be something. The assertion "S is not" 
is on the one side either entirely false, or, on the other, more than 
idle — just empty breath. If 8 were just nothing at all, it would 
be meaningless to say "S is not." Bring is the general attribute 



50 FOOTNOTES TO FORMAL LOGIC 

thai belongs to anything thai can stand as subject of a proposi- 
tion. This truth was expressed in an earlier paragraph in the 

statement that in every judgment there is unmistakably present 
to thought a something. The judgmenl "S is /\" means to assert 
that reality lias the characteristic, 8- P. 3 



II 

In considering the nature of the concept or idea we saw that it 
is difficult to discover any difference in kind among the cognitive 
states of consciousness, from simplest concept to the most com- 
plex judgment. That the concept seems to shade by imperceptible 
gradations into the judgment was recognized by Aristotle and 
before him. And in the modern discussions we find writers who, 
having defined the concept and the judgment in static terms, 
in independence of each other, are much embarrassed by the 
discovery of forms of thought that refuse to be classed as either. 
There are forms which have already burst the conceptual shell 
and yet are classed as concepts ; and, on the other side, there are 
forms which are classed as judgments that are lacking in the 
essentials of judgment. The recognition of this distinction led 
Bain to call the verbal proposition the "notion in the guise of a 
proposition." 

Nevertheless, when one describes thinking as a movement 
from the particulars of concrete sense experience to conceptual 
universalis, he disregards a most important aspect of the knowing 
process. In its analytic attention thought makes distinctions (or 
we should say, heightens distinctions already vaguely present), 
and these distinctions when synthesized form the generals. But 
this is only one-half of the process. These abstractions which 



■ Plato long ago pointed out the paradoxical fact that when you call 
:i thing a ii on entity, a mere illusion, you do not thereby get rid of it. 
There is a deep metaphysical significance in tlie remarks of the colored man 
passing by a church yard ;it night: "I don't believe in ghosts nohow, 

hut I hope they never find it out, it might make them mad to think a fellow 

didu 't believe in them. 



THE IMPOET OE JUDGMENT 51 

lie at the end of the movement in this direction are not kept in 
cold storage, but are thrown back again upon the concrete 
instances from which they arose. And in this return movement 
the concepts, or universals, always put a new meaning into the 
concrete instances. Nevertheless, in this reciprocating movement, 
thought is not acknowledging its inadequacy to reality. This 
is not a make-shift, or compromise, confessing thought's incom- 
petence : it is an exhibition of the highest type of control of 
reality. A transverse cross-section, so to speak, of the movement 
would reveal the seeming contradictions of idleness and falsi- 
fication. Any moment of the process would exhibit tautology, or 
novelty, when detached from its setting in the whole. But a 
longitudinal section would reveal the true nature of the process 
in its totality, where the tautology, in the light of the anticipated 
novelty, is not to be condemned as idle ; and the novelty, resting 
back on the identity, rescues the judgment from the charge of 
falsity. 

As bearing upon our search for the essence of judgment we 
may revert to the significant distinction that has often been made 
between knowing and understanding. It is alleged that we are 
here dealing with thought processes that are sufficiently different 
to require two different words. Understanding is a later and 
and higher phase of thinking. We have understanding when we 
appreciate or evaluate knowledge, when we know that we know, 
and why we know. Although the distinction between the two 
kinds of knowledge has frequently been pointed out, there has 
not been offered, it seems to me, a convincing account of their 
relation. Bearing in mind that these words represent stages in 
the development of knowledge, and therefore have something 
in common, the question at issue in the relation between the two 
types of knowing is What precisely have they in common? Are 
they different in kind or are they, as has been remarked, an 
earlier and a later stage in what is essentially a simple process? 
That there are these two kinds of mental activities is evidenced 



FOOTNOTES TO FORMAL LOGIC 

by the fad thai most Languages have two different wards to 
represent them: scin and cognoscere, in Latin; kennen and 
wissen in German; savoir and connaitre in French, stand for 
these two kinds of knowing. In English, in addition to the words 
knowing and understanding, we have several aspects of the same 
distinction expressed in the phrases, "knowledge of acquaint- 
ance" and "knowledge about." 

It will be well to examine more closely the difference that is 
here intended. We need to discover, if possible, the point at 
which there is a change in kind as we pass from the lowest form 
of sensory judgment to the highest type of reflective judgment. 
Knowledge of things by acquaintance is not far removed from 
Hegel's unrelated immediacy; it is just simple apprehension 
or existential awareness. But now all who have ever attempted 
to describe and explain this simplest form of knowledge have 
admitted the difficulty in giving it any logically independent 
standing. It seems to have no existence apart from the higher 
knowledge, the knowledge of truth. Even Russell, while claim- 
ing logical independence for the knowledge of acquaintance, 
says: "It would be rash to assume that human beings ever, in 
fact, have acquaintance with things without at the same time 
knowing some truth about them.' 7 All that we seem justified in 
saying is that we find these two distinguishable, but not separable 
stages in the natural course of thought — first immediate aware- 
ness, then being aware of the awareness. I can think, and then [ 
can think or recognize that that is one of my thoughts. The sec- 
ond, or complex stage is the stage of description, definition, evalu- 
ation. But already in the first or simple stage there are implicit 
these characteristics which on the reflective level have become 
explicit. 

This distinction between the two types of knowing we have 
in Professor James' familiar illustration of the difference 
between cognition and recognition. A bird flutters against my 
window pane, and I acknowledge the event in its first stage of 



THE IMPOET OF JUDGMENT 53 

immediate awareness with "Hello, thing-a-bob. " And in the 
second stage of evaluation I say, "Ah, robin." But even here, 
is the difference more than relative ? Is the transition from one 
pulsation of consciousness to the other marked by any difference, 
in kind? The first judgment is in the form of S is P in which 
there is already a partial definition which the second judgment 
S is P only makes more explicit. 

Some writers suppose that there are in the thought process, 
more than the two stages we have just considered. Adamson 
says: "The real order is sensation and sensory judgment, con- 
ception, memory and memorial judgment, experience and experi- 
ential judgment, inference, inferential judgment, inferential 
conception. ' ' 4 But the more stages one marks out in the process 
the more does one emphasize the fact that consciousness is a 
single continuous affirmation in which there is nothing at the 
end of the process which was not also present at the beginning. 
In other words, there is no distinction between beginning and 
end. We may read off the story of our analysis in either direc- 
tion, thus revealing the true nature of thought as the exhibition 
of a whole through its genuinely simultaneous differences. 5 
Temporal arrangement in the proposition is an entirely different 
thing from logical coherency in the judgment. The relation 
between the parts of a logical whole is unique, it is altogether 
different from sequence of time and from contiguity of space. 
Logical coherence has been confounded with sequence in time 



4 Encyclopedia Britannica, XVI, 880. 

sCf. Bradley, in Mind, n. s., XVII (1908), 170. "The content of the 
judgment is one thing and its psychical duration is another thing, and in 
principle we have seen that the duration is irrelevant. But on the other 
hand every judgment is a psychical event and has therefore duration. 
Wholly to deny this aspect seems a fundamental error." 

Cf. Bosanquet, Essentials of Logic (London, Macmillan, 1895), p. 73. 
' ' The separate existence of the spoken or written word, produces an illusion 
which has governed the greater part of logical theory so far as concerns 
the separation between concept and judgment, i.e., between entertaining 
ideas and affirming them in reality. In our waking life, all thought is 
judgment, every idea is referred to reality, and in being so referred, is 
ultimatelv affirmed of realitv. " 



:. i FOOTNOTES TO FORMAL LOGIC 

and with contiguity in space, because in speech and in writing 
we do produce mental and physical symbols subject to time and 
space" But il should be remarked thai it is not sufficient 
to say that in most modern and highly developed languages, the 
subject, predicate and copula in the proposition are separate 
words, while in the ancient and undeveloped languages they are 
welded together in a single form. Some explanation of the 
phenomenon should be offered. If "I am loved" is equivalent 
to amor, it would be interesting and important to know what 
principle of evolution has produced the former differentiated 
expression. Is it entirely a phenomenon in the growth of 
language, or is it vitally connected with certain stages in the 
movement of the judging process itself? 

No judgment can ever become so complex as to escape 
embracement in a single idea. But the related parts of this 
enwholing idea are not themselves just ideas in relation. Judg- 
ment is not merely the affirmation or denial of a relation between 
the two ideas. This has been pointed out so frequently in recent 
discussions that I need only refer to it in passing. When I 
assert that an automobile is going down the street, I do not mean 
that my idea of an automobile is traveling down my idea of a 
street. What I mean to affirm is that the objective world does 
have in it a complex of related facts which I characterize as 
automobile-going-down-the-street. But, as I have already in- 
sisted, the object to which the idea refers its content is in no 
wise alien to that idea. Every idealistic theory of judgment 
must of course hold that this object is just the self-transcending 
character of the idea. What I wish to emphasize is the fact that 
the ideas between which the relation exists are not the same in 
kind as the idea within which the relation is embedded. A dis- 
persive category operates in the former instance and a synthetic 
category in the latter. 



THE IMPORT OF JUDGMENT 55 



III 

Among the disputed problems lying on the borderline of 
Psychology and Logic is the question, which we have already 
noted, of the difference between perception and the perceptive 
judgment. Bradley and others have insisted upon the impor- 
tance of distinguishing between these tw T o mental states. We 
have already discussed one aspect of this subject. In pure per- 
ception there is a direct reference to an object, which is a datum 
in the etymological sense of the word. The object is something 
given to the subjective activity independent of that activity. The 
perceptive judgment, however, is an inner ideational process 
proceeding from the spontaneous activity of the subject, in 
response to or as a reaction upon the perception. The difference 
lies in the essential distinction between activity and passivity. 
The ultimate object in every assertion or enunciative act of con- 
sciousness is an individual. In the perceptive judgment this 
objective is given to thought directly, and implies the existence 
of two things only, namely, that object and the mind that thinks 
it. But in the cognitive or reflective judgment the object — again 
an individual — is given indirectly. In the reflective judgment 
the object is only vicariously present in the concept, to which 
concept other like objects have already been given and to which 
future objects may in turn be presented. The transition from 
perception to perceptive judgment is made in the interest of com- 
munication. 

The proposition as the outward expression of the inward fact 
of judgment is primarily an instrument of intercourse — its func- 
tion is purely social. 7 It begins with an undifferentiated whole 
in the position of subject, and concludes with this same whole 



" Windelband has laid great stress on the social character of knowing. 
"Perceiving and knowing," he says, "as empirical functions are entirely 
social in their nature. They are integral parts of the common mental life — 
for the lonely strivings after truth of the individual are a late product of 
civilization which is always rooted in some historical community of knowl- 
edge and tends to discharge itself into it again." Ency. Philos. ScL, I, 617. 



FOOTNOTES TO FORMAL LOGIC 

differentiated into members, one of which takes its place in the 
position of predicate. The analysis of this undifferentiated 
whole is what the speaker accomplishes, when by means of a 
descriptive, elucidative, or demonstrative judgment, he under- 
takes to instruct his hearers — when as we say he communicates 
information. Now the logician who stresses the non-temporal 
character of judgment finds it difficult to account for these differ- 
ent meanings that are found at the two significant dates in the 
life history of the subject, namely, its meaning before and its 
meaning after the differentiation. The judgment is thus seen to 
be neither exclusively temporal nor non-temporal. It may be 
both without contradiction. 

The failure to recognize this fact, namely, that the judgment 
claims to be both temporal and non-temporal has throw r n the 
new theories into hopeless confusion. The judgment is not in 
time, but the judging is. The judgment in the speaker's mind, 
prior to his determination to express its meaning — to tell his 
hearers something — is not in time. But the judging, which 
unfolds itself outwardly in the proposition is in time. The 
empirical theories of judgment have with right insisted that 
there is a sense in which the judgment, or more accurately the 
judging process must be regarded as in time. But this temporal 
expression of itself is just the standing reminder of the irra- 
tionality of sense, or the ill-adaptation of conception to percep- 
tion. If thought were entirely adequate to the task of communi- 
cation, it would not adopt this apparently self-contradictory 
device for its outward expression. But the a-priorist has also 
rightly insisted that the judgment (not the judging) is non- 
temporal. It has no parts that may be arranged seriatim like 
the pa its of a sentence. The relation between subject and 
predicate is not a relation between successive mental states, but 
is its. ']f a unitary progressive state. 

Professor Schiller says "We have steadily kept in view the 
Eacl that Judgment is the primary act of thought and that the 



THE IMPOST OF JUDGMENT 57 

attempt of Formal Logic to 'analyse' it into something more 
elementary is a fictitious procedure, which can be justified only 
by its convenience and success. s Now many who are distinctly 
not pragmatists would agree entirely with Professor Schiller 
that judgment is the primary act of thought, and that only by 
abstraction can we arrive at anything more elementary. Also 
in the majority of the ordinary textbooks, where the first chap- 
ters treat of terms and ideas, the authors are careful to point 
out that such discussions belong properly to philology, and to 
psychology. Even Jevons who is so outspokenly an associa- 
tionist in his view as to the nature of the thinking process says : 
"The continued study of Logic convinces me that this doctrine 
of terms is really a composite and for the most part extra-logical 
body of doctrine. 9 

It is true, as Aristotle remarked, and as since then so many 
logicians have repeated, a word has no reality in living language, 
and the idea no reality in living thought. We must not regard 
the proposition as a synthesis of words, nor the judgment as a 
synthesis of ideas. And yet, when once the act of judging has 
been performed a retrospective analysis discovers ideas to be 
different, but not separate aspects of the judgment. 

The data of knowledge appear to come in a stream of isolated 
sense-presented facts, which the mind is called upon to weld 
together into wholes of ever increasing complexity. The 
sequence in the mental states seems to be first the idea A, then 
the idea B. and lastly the judgment A in relation to B. Some of 
the older empiricists were bold enough — even in the face of 
the insurmountable difficulty at the third stage — to say that such 
a process of crystallization by the external accumulation of ideas 
is the true explanation of the thinking process. But the impossi- 
bility of ever achieving any real continuity in this process of 
knowing things together, led the later associationists to substi- 



- "Formal Logic, p. 92. 
§ idles in Deductive Logic, p. 1. 



FOOTNOTES TO FORMAL LOGIC 

tute analysis for synthesis as the central function of thought. On 
this view the most elemental judgment — or if we are not pre- 
pared to call this primary state a judgment — the most primitive 

datum of knowledge is an undifferentiated feeling or sensation. 
Judgment then, is not a combination of two ideas into one, but is 
the separation of this primary undifferentiated feeling into its 
two correlated aspects. But this analytic process is also embar- 
rassed by at least three unmanageable difficulties : ( 1 ) What 
precisely is the original feeling, (2) what is the principle of 
differentiation and how does it operate, and (3) what are the 
two facts or aspects to which the division leads? 

The ancient dilemma of ignava ratio which conceals the 
fallacy of incomplete disjunction has been perpetuated in the 
modern attack upon the validity of judgment. Predication is 
discredited today in almost the identical language of the 
Sophists. Either our predicate is contained in the subject or it is 
not. If it is not, we have no right to say that the subject is the 
predicate, and the judgment is false ; if the predicate is already 
in the subject, the judgment is idle. Now I submit that this 
argument is cogent only in the sphere of quantity where the term 
"contained in" has application in an intransitive relation only. 
In the quantitative world an object cannot be both inside and 
outside of a class. But the relation between subject and predi- 
cate in judgment depends upon a totally different conception of 
a class. The two alternative positions in which the predicate is 
placed in the ancient dilemma — inside or outside the subject — 
do not exhaust the possibilities. With a different conception of 
the relation of a term to its class the predicate may be both inside 
and outside of the subject; there is both novelty and identity 
in judgment — stability and risk. This very important subject 
of novelty and identity in judgment I propose to discuss farther 
in a special chapter. 



THE IMPOST OF JUDGMENT 59 

IV 

It will not be necessary for the general purpose of this inquiry 
into the nature of judgment to go into any detailed consideration 
of the perennial question as to whether the class view of predica- 
tion is logically fundamental. I shall discuss the class view of 
predication and the subject of the relation of extension to inten- 
sion in considering the validity of the syllogism. I must, how- 
ever, point out at this time what seems to be a very prevalent 
mistake in the more recent criticisms of the class view. "Windel- 
band says : 

As far back as Aristotle, Logic has given way to the temptation of 
regarding the subject thus conceived as falling within the sphere of the 
predicate as the type of all judgment, and subordination or subsumption 
as the prevailing meaning of the copula. This is an error in principle of 
the scholastic logic, "Gold is a metal," is indeed a real subordination; but 
' ' Gold is yellow ' ' never means in living thought that gold ought to be 
subsumed under yellow, which would be obviously nonsense — and certainly 
not always that gold is to be reckoned among yellow bodies, but rather that 
gold has the property of yellowness. Subsumption may be thought of as a 
side issue, but it is not the precise meaning of the judgment. 10 

Windelband has failed, in my opinion, to state the precise 
grounds of the distinction between a "side issue" and a "pre- 
cise meaning." If these two expressions are to be taken as 
synonymous with "essential" and "accidental," then by defini- 
tion the side issue or accidental characteristic of judgment 
cannot be regarded as the prevailing meaning of the copula. But 
if the side issue is always an essential side issue, that is, if 
it is a real property in the scholastic sense, we may for certain 
purposes consider it the precise meaning and relegate the former 
precise meaning to the position of side issue. If the judgment 
has various meanings, all equally present, by what criterion shall 
we decide between the primary and the secondary meaning — the 
precise meaning and the side issue. How much we mean when 



u>Ency. Philos. Set, I, 37. 



FOOTNOTES TO FORMAL LOGIC 

we say "all men are mortal," how we reach these meanings, and 
how we rank them in importance, is the basic question in Logic. 
This distinction between the main issue and the side issue, 
the bona fide meanings and the spurious meanings has been car- 
ried into the distinction between the problematic and the apo- 
deictic judgments. Professor Sidgwick lias said: "No propo- 
sition can, after all, be more than true; that no piling up of 
adverbs like 'certainly' or 'necessarily' will intimidate the actual 
facts." Bui the modal adverbs, I submit, have no intention to 
•intimidate the facts": they apply to the thought about the 
i'aets, not to the facts themselves. The attempt to dispense with 
modality in propositions rests back upon the denial of the 
scholastic distinctions between rationes cogsnoscendi and rationes 
essendi. The reasons for knowing, or perhaps we should say 
the reasons for belief, may vary from the zero of pure doubt 
to entire conviction. The reasons for being exhibit no such 
gradations. It is, indeed, a contradiction in terms to speak of 
reasons for being. But there are, and must be, reasons for 
knowing, and when knowledge searches for its reasons it epitom- 
izes these supporting or inferential judgments in modal adverbs. 
The necessity in apodeictic judgments depends upon scientific 
or demonstrative evidence, while the necessity in assertoric judg- 
ments depends solely upon enumeration or observation. 

The act of comparison which our theory regards as the pri- 
mary function of judgment is not so simple a process as on the 
surface it appears to be. Comparison involves cross-reference of 
one object to another, that is, each object submits to being 

ssed by a principle which is inherent in the other object. 
Bosanquet thinks that comparison is not necessary to every judg- 
ment. Comparison he holds can not be expressed with complete 
convenience in a single judgment. Now it is true that the com- 
paring act is not evident in the judgment in its simple form; 
hut when the entire content of the judgment becomes explicit 
] i Eh in' ntary Logic, p. 71. 



THE IMPOST OF JUDGMEM 61 

and it is made fully aware of its reasons, then comparison is seen 
always to lie at its heart. 

More is needed for an act of judgment than just the juxta- 
position of subject and predicate in consciousness. Comparison 
means more than simple association. The association theory of 
thought is incapable of bridging the gap between the two facts, 
taken simply as facts in relation. Thought must betake itself 
to the circumambient universal at each step. However, the 
universal which is thus operative in each particular state of 
consciousness is not always manifest. As Bosanquet has said: 

Its operation is extended throughout a series of the fugitive psychical 
facts or ideas, and although in logical thinking its operation is conscious, 
i.e., selects and modifies within the content of these ideas, yet it is not in 
itself necessarily a conscious activity. It acts in consciousness, but need 
not be conscious of its own principle of action.12 

y 

The teaching of ordinary Logic, that every proposition is a 
sentence but not every sentence is a proposition, is not entirely 
free from criticism. It is alleged that only the declarative sen- 
tences are true propositions. But every sentence has a mean- 
ing, even the imperative, optative, and exclamatory sentences; 
though these, to be sure, cannot be said to be either true or false, 
in the form in which we find them expressed. The old familiar 
definition of a sentence — that it is an expression of thought in 
words — tells a hidden truth about those forms which are com- 
monly not admitted to the rank of real propositions. A thought 
is always implied in every command, wish, or exclamation. A 
complete analysis of the states of consciousness corresponding 
to the various so-called sentences would reveal both a cognitive 
and an emotional aspect in each. In the indicative mood the 
cognitive characteristic is overt and the emotional characteristic 
is implied. In the other moods the emotional aspect is expressed 



12 Logic, II, 6. 



hi 1 FOOTNOTES TO FORMAL LOGIC 

and the judgment, or assertion, or cognitive characteristic is 
implied. The exclamation "fire," the command, "avaunt," the 
wish "a horse! my kingdom for a horse," each implies an 
assertion which is not expressed. Instrumental Logic is quite 
right in maintaining thai for the purposes of complete definition 
and in our practical lives we should take into account these 
implications. But it is wrong, in my opinion, to assert that 
it is impossible to detach the cognitive factor for exclusive 
study. 

A state of consciousness may be simple and unequivocal while 

its outward expression may be duplex, that is to say, one judg- 
ment may require for its expression two propositions. And on 
the other hand there may be a multiple content in mind — two 
or more judgments — with only one proposition to represent 
them. Illustrations of the former we find in the rhetorical 
devices for securing emphasis through tautology, repetition or 
elaboration. "The last rose of summer is gone. It is fled," 
are two sentences or propositions, but one judgment. "All the 
planets except Venus and Mercury are outside the earth's orbit," 
"None but the brave deserve the fair," are duplex propositions. 
Each is in form a single sentence containing two assertions. The 
name cxponible which was given by the older logicians to these 
propositions with multiple meanings w r as etymologically some- 
what unfortunate. Any of the more modern words plurative, 
duplex or portmanteau propositions is to be preferred. A care- 
ful analysis of these portmanteau propositions, particularly the 
exclusive propositions, which are either omitted or given only 
slight consideration in most discussions of the import of proposi- 
tions will throw light upon the nature of judgment and of infer- 
ence. In the exclusive proposition "None but the brave deserve 
the fair," we have the interesting situation of two judgments 
and two propositions telescoped into one sentence. It is likewise 
interesting as an illustration of an attempt on the part of the 
speaker to recognize the existential import of propositions but 



THE IMPORT OF JUDGMENT 63 

to provide, in the form of the assertion, for a non-committal atti- 
tude toward the question of the existence of the subject. 

It is often said that the educational value of elementary 
Formal Logic consists chiefly in the exercise of paraphrasing 
poetical or rhetorical assertions into the type-forms of proposi- 
tions, with the least possible sacrifice of meaning. I do not think 
this is true. The translation of propositions from their rhetorical 
to their logical form is a literary occupation. This is a task that 
properly belongs to the grammarian and the philologist, not to 
the logician as such. This is an interesting and important work, 
but it is no more the special business of Logic than the transla- 
tion of a foreign language would be. The translations of propo- 
sitions should be distinguished from their transformations. The 
task of the logician begins after the student of language has 
translated the poetic or rhetorical form into the type-proposi- 
tions. He has the task, then, of transforming the standardized 
proposition into its various implications. Logic is the science 
of inference, not the art of translation. Given an unequivocal 
type-form it is the business of the logician to classify all the 
other propositions that deal with the same subject and predicate 
as true, false or doubtful. And this involves an intellectual 
discipline of great interest and value. The recent successful 
developments of Symbolic Logic exhibit more truly the proper 
scope of Logic, than does Genetic or Instrumental Logic. I 
repeat the criticism so often made, that the latter is not Logic 
but Psychology. 

An excellent illustration of the failure to distinguish between 
Grammar and Logic is found in Dr. Mercier's treatment of 
propositions. He writes: 

For logical purposes, the most important distinction between different 
propositions is that between the Incomplete and the Complete. This is a 
distinction new to Logic, but it is one of the greatest importance. An 
incomplete proposition is, as its title implies, a proposition of which an 
element is missing. Every proposition expresses a relation ; and, as we shall 
find further on, a relation consists of three elements — two related terms, 



• it FOOTNOTI-S TO FORMAL LOGIC 

and the ratio which expresses the relation between them. Any one of these 
elements may be missing. ... in the proposition "A is B," the term A 

ntav be missing; but we can keep the proposition in form until the missing 
element can be supplied, and at the Bame time introduce a reminder that 
the term is missing, and needs to be supplied, by putting in place of the 
missing term the relative ''what.'' By this means we obtain the incom- 
plete proposition, "What is B. " Similarly, if B is missing, we can throw 
the incomplete proposition into the form, "A is what?" These are mani- 
festly questions, and should be characterized as questions by the addition 
of the interrogation sign; and we then get the incomplete propositions, 
"What is B?" " A is what?" which at once preserve the form of the 
proposition, and remind us that the proposition is incomplete and clamors 
for completion. !3 

Here it seems to me, Dr. Mercier has disregarded the vital 
distinction between a question and a proposition. He is quite 
right in asserting that all propositions are preceded by questions 
of some sort. The question may, indeed, be most vague and 
amount merely to a psychological restlessness, but this question 
is one thing, and the assertion that follows upon it quite another. 
If instead of writing these so-called propositions as a question, 
for instance, "What is B?" he had written it as an assertion, 
"Somewhat is B," he would have been closer to the facts as we 
find them in the mind. These so-called incomplete propositions 
correspond not to incomplete but to indefinite judgments. It is 
not true that there is no subject but that the nature of the asser- 
tion is such that we are not able or not concerned to specify it. 
The whole meaning of the judgment has gone over into the 
predicate, and in the subject position we have a that without a 
what. This, I believe, is the true account of the impersonal 
propositions. 



w Logic, p. 30. 



THE IMPOST OF JUDGMEN I 65 

VI 

Every judgment claims to be true ; if it did not, it would 
forfeit its right to be called a judgment. This claim to be true, 
means that the mind that judges distinguishes between idea and 
object, in recognizing that it might have an idea which is not in 
agreement with the object. Here, again, it is necessary to dis- 
tinguish between a judging consciousness and one that merely 
apprehends. The difference between the two is that one con- 
fesses the possibility of error, while the other knows nothing 
of the distinction between truth and falsity. There is an essen- 
tial difference between the simple apprehension "This is A," 
and the judgment, "This is A." The judgment is never merely 
the awareness of something present. It asserts qualities that 
are derived from relations which transcend the present. And 
in this reference to facts not present there is the risk and the 
possibility of error which differentiates the judgment from the 
apprehension. 14 

Error is the most perplexing subject in the whole field of 
Philosophy. Why does it exist? Or is there perhaps no such 
thing as error, as the sophists alleged? Plato felt called upon 
to devote an entire dialogue to the refutation of the sophist's 
view and after twenty-three centuries the new realists find it 
their most embarrassing problem. There would truly never be 
any error, we should never make mistakes in judging, if we 
never took any risk in the predicate, if we always said "A is A," 
and never attempted to predicate of A something other than its 



I* On this point see Sidgwick, Elementary Logic, p. 196. "This risk, 
then, is always present when we make a predicative statement, however 
carefully worded the statement may be. There is no way of escaping it, 
short of ceasing to make any predications at all. It is the price we pay for 
the power either of generalising or of describing a Subject; it is a defect 
that belongs to a quality. ' ' I should agree entirely with this account of 
the essential risk in judgment, but should differ as to its interpretation. In 
the chapter on "Novelty and Identity in Inference" I have tried to show 
that the risk in judgment is not destructive of a stability t'.xat is just as 
essential as the risk. 



66 FOOTNOTES TO FORMAL LOOIC 

bare identical sell', something genuinely different from it. But 

we do take the risk and must lake it. And it is the business 
of critical philosophy to ask for the reason why we take the 

risk and what is the success of our venture. We see at once, 
that the modern query, "How can one mind contain both the 
possibility of knowledge and the liability to error? 1 ' is identical 
with Kant's fundamental problem, "How are synthetic judg- 
ments a priori possible?" and this in turn is the same as Plato's 
question, "How can we affirm of a subject a non-identical 
predicate!" 

It is very easy to state the difficulties about error, but far 
from easy to remove them. The Law of Excluded Middle 
declares that reality and non-reality exhaust the entire universe. 
Now from the purely subjective point of view, that is, before we 
attempt to classify any of the facts of universe, this law is com- 
pelling. A thing is either real or it is not real ; we cannot accept 
anything between these two. When, however, we begin the 
process of classifying subjective and objective facts, on this 
principle, we get along very w r ell until we come to the group of 
negative conceptions among which error is found. These stub- 
bornly refuse to go into either of the two aforesaid classes. 
Error, for instance, refuses to be classed as either reality or 
non-reality. It insists upon having a third place made for it, 
for which as w T e have just seen, Logic at the outset makes no 
provision. There is truth in the remark that error is the occu- 
pation by an actuality of a place which does not exist. 

Thus does thought discover a most interesting dilemma about 
lh on f/ht. It can compel truth to reveal its own intrinsic false- 
hood. Also it can extract from error the confession of its essen- 
tial reality and necessity. To put it otherwise, in the manner 
of Bradley, an appearance which is, must fall somewhere. But 
error, because of its intrinsic negativity cannot belong to reality, 
and again, it can not belong to appearance, because that, with all 
its contents, cannot fall outside the Absolute. An appearance 



THE IMPOST OF JUDGMENT (37 

entirely outside of Reality is naught. The essential character- 
istic of falsehood, error, fiction, is that an actuality should claim 
to be something other than itself. Many of the popular wit- 
ticisms are based on this fundamental paradox. For example, 
the definition of a liar as one who tells the truth about something 
that never happened. It will be observed that I have differed 
from Bradley as to the place of error in judgment. He con- 
tends 15 that we can not, while making a judgment entertain the 
possibility of its error. One can not judge and doubt at the 
same time. I have insisted that one does not judge unless one 
does feel the actual constraint of a doubt. 



is Mind, n. s. XVII (1908), 154. 



CHAPTER IV 
NEGATION AND THE INFINITE JUDGMENT 

I 

There are four possible ways in which we may regard the 
relation between the affirmative and the negative judgment. We 
may hold that: (1) each is an independent and final form of 
thought's functioning — original, underived and self-directing; 
(2) negation comes after affirmation and is the result of a 
thwarted affirmation; (3) affirmation follows negation and is 
what we find left over after negation has destroyed certain 
possibilities; (4) affirmation and negation are correlated aspects 
of a more fundamental form of thought. 

The first is the view of common sense and need hardly be 
discussed, although it is the innocent presupposition of some 
systems of Logic. It has been included in this fourfold classi- 
fication for the sake of formal completeness. The second view, 
which makes negation subordinate to affirmation, has had many 
advocates, notably Sigwart and Erdman. The third doctrine, 
omnis deterndnatio est negatio has had able defenders from 
Spinoza to Venn. Although this controversy concerning the 
logical priority is many centuries old, the supporters of the 
second and the third views are still quite equally divided, which 
suggests that each side has hold of one aspect of a multiple truth. 
The fourth position maintains that neither affirmation nor nega- 
tion is logically prior, and that while each necessarily involves 
the other, both are dependent upon a more central form of 
thought. Tli is view makes possible, it seems to me, a genuine 
reconciliation of the divergent claims of (2) and (3). 

Sigwart 'a view that every negation presupposes an affirm- 
ation, has been characterized as "monstrous" by Bosanquet. 

[68] 



NEGATION AND THE INFINITE JUDGMENT 69 

However, we must admit this is a true and accurate description 
of a stage in the complex whole of the judging process. That 
reality is a system of inter-related facts is a postulate of every 
judgment. This affirmation of an orderly whole which is the 
logical presupposition of every specific judgment, always takes 
the form of a disjunctive judgment. It is an assertion to the 
effect that reality offers alternative possibilities to the judging 
consciousness. "S is either P or non-P." Bosanquet 1 and 
Bradley 2 are doubtless right, however, in saying that this postu- 
late can not properly be called an affirmative judgment. Judg- 
ment implies belief and we can hardly be said to have judged 
and "believed' ' when the mind is poised between the balanced 
terms of a disjunction. 

This postulate, or disjunctive affirmation, which precedes 
the negation is not the same in kind as the affirmation which 
comes after the negation. They differ as suggestion differs from 
assertion. It is true that in the life history of the judging 
process negation does occur between two affirmative states. But 
the one is an ideal construction and the other an affirmation of 
fact. The prior disjunctive judgment is a crucial instance, 
and has the same structure as a genuine hypothesis in science. 
It is strictly non-committal. It has been said that the suggestion 
in the disjunctive judgment is the same as the assertion that 
remains after the selective process of negation. This is the only 
view that lends support to Sigwart's doctrine, but this is clearly 
untenable. We can not say, as Sigwart's view would have us 
say, that negation is the rejection of an actual judgment. The 
acceptance of the bare presentation of the choice between alter- 
native possibilities is not a judgment. 

Bosanquet says, "Every significant negation, S is not P can 
be analysed as S is X which excludes P." But now we may 
properly ask "At what stage has the exclusion taken place?" 



i Logic, I, 321. 

-Principles of Logic (London, Paul, 1883), p. 110. 



FOOTNOTES TO FOBMAL LOGIC 

[f there is no necessity for putting the verb is and excludes in 

tlic same tense, we may consider the exclusion to have been per- 
formed first and thereafter the discovery made thai the inclu- 
sion of .1 in X had been affected thereby. The complex judg- 
ment would then read as follows: A (B having been excluded) 
is found to be X. This obviously would be a return to Venn's 
Theory of Judgment. Again we might stress the inclusion and 
say: .1 (in being X) has excluded B. The vital question is 
whether the exclusion is before, after or simultaneous with the 
inclusion \ The logical analysis of the content of consciousness 
does give support to the view that the only meaning of any 
affirmation of a proposition is found in what it denies. Actuali- 
ties can not be asserted, they arise spontaneously out of, or by 
the side of, the destroyed possibilities. The actualities we seem 
to get by the way of pure affirmation are always pseudo-actuali- 
ties ; they have never more than a hypothetical existence. And 
yet on the other hand, the psychological analysis always finds 
negation at a point farther from reality than affirmation. 

The logical negative does in fact always contradict, but in 
contradicting never affirms the reality of that which has been 
denied. The dichotomy which is at the bottom of every nega- 
tion, begins with existential reality, but in breaking up the 
whole into parts it is powerless to keep in each part the full 
measure of the reality of the whole. 8 The assertion that "S is 
not P" is the same as the denial that S is P, and both are equi- 
valent to "S is P is false." And in no one of these three 
equivalent statements has thought passed beyond P into non-P. 
No assertion is made about the reality or the non-reality of P. 
Bradley has maintained that negation can not in any way be 
derived from affirmation, nor affirmation from negation, and yet 
he thinks it wrong to consider them coordinate species of a 
higher form. But although he is unwilling to accord to either 
tie- prior position in Logic, in Psychology he places negation 



b Cf . Bradley, "Principles of Logic, p. 118. 



XEGATIOX AXD THE INFINITE JTDGMENT 71 

after affirmation. Since negation presupposes a positive ground, 
he says, "it stands at a different level of reflection." And this 
again is in accord with the view expressed earlier. No difficulty 
is found when we observe the distinction between the logical and 
the psychological aspects of judgment. 

When Bradley says "Nothing in the world can be denied 
except on the strength of positive knowledge," he is after all 
admitting the main contention of those who hold that negation is 
a thwarted affirmation. It is true, as has already been shown, 
that the prior affirmation which he concedes does not refer the 
ideal content to reality with the same claim to truth as the 
later affirmation, namely, that which selects from among the 
presented alternatives. The first is a suggested affirmation while 
the second is an asserted affirmation. But Sigwart himself 
recognizes the essential difference between these two forms of 
affirmation when he says, "The primitive judgment should not 
be called affirmative at all ; it would be better denoted as positive. 
The simple statement A is B is an affirmation only when opposed 
to the negative judgment." In view of this explicit statement 
I do not see why Bradley finds Sigwart 's doctrine so "obviously 
absurd.*' 

There is a prevalent tendency, especially in the elementary 
textbooks of Logic, to define affirmation and negation in terms 
of approval and disapproval. This is not precisely accurate, for 
there is also an aspect of approval latent in every negation. We 
accept negation as true or false, and thus approve or dis- 
approve 4 It is impossible in thought to draw a line between 
affirmation and approval. We do not first affirm, and then, after 
having contemplated the object of our affirmation, pass to a 
second act of approval. Approval and affirmation are simul- 
taneous. In discussing the relation between apprehension and 
judgment, we saw reason to distinguish between mere acknowl- 



* On this point see Sigwart. Logic; translated by Dendy (ed. 2; London, 
Macmillan, 1895), I, 381. 



72 FOOTNOTES TO FORMAL LOGIC 

edgment of a contenl without critical reaction, and true judg- 
ment or acceptance through criticism. Bui this we held was a 
theoretical distinction entirely. In living thought there is a 
simultaneity in the midst of the succession. 

II 

The infinite judgment lias been much discredited. Since it 
attaches no positive and definite characteristic to the subject, 
it has been condemned as idle, practically worthless, and even 
illogical. Honesty is non-blue, for instance, is meaningless, 
because the negative term includes all possible predicates other 
than blue and does not even so much as insist upon the existence 
of the predicate. It is the farthest limit of indifference. This 
doctrine of the essential irrationality and futility of the infinite 
judgment is very old. ■ By some it has been traced back beyond 
Plato to Anaximander. But I must point out at once, as bear- 
Plato to Anaximander. But I must point out at once, as bear- 
ing upon a later defense of the infinite judgment, that the cnretpov 
of Anaximander was a positive infinite, and by him regarded 
as the source or original of all things. Modern writers think 
they find justification for the contempt which they heap 
upon the infinite judgment in Aristotle's own treatment of 
the subject. But we may doubt whether Aristotle would have 
approved of this later-day entire condemnation of the infinite 
judgment. This problem first presented itself to Aristotle in 
his discussion of terms. He saw as plainly as any one since his 
time that there is a paradox about the negative term. It must 
be defined as a term which implies the total absence of a 
quality. Technically speaking it connotes the absence of conno- 
tation. It is the self-contradictory attempt to make something 
out of nothing. 5 



5 Bosanquel has stated the dilemma with admirable clearness: "The 
Negative Judgment presents at first sight a paradoxical aspect. We are 
bound to take it, qua judgment, as playing some part in knowledge, and 



NEGA TIOX AND THE INFINITE J I DO .17 EN T 73 

It is alleged to be a self-contradiction to say that a term may 
connote just the absence of a quality. It is not strictly speak- 
ing true, we are told, as is often supposed by the opponents of 
bare denial, that no term can be purely negative. But now it 
depends entirely on what we mean by a purely negative term. 
The class of privative terms, which logic has been compelled to 
recognize from the first, is a genuine class ; and the definition of 
this class of terms must be greatly strained to allow even a 
modicum of positive quality in a privative term, in the ordinary 
interpretation of the word positive. A positive character of an 
entirely different sort it does possess. The negative term denotes 
an object which in the first place lacks the qualities denied by the 
negative term but has other qualities in terms of which that 
very lack is defined. Every negative must have a positive basis. 
A sheer naught can not be the ground of a denial. Non-P will 
always signify what an object will be, which might be P, but is 
not. But granted that these so-called privative terms do have 
a genuine positive connotation, even if slight, there seem to be, 
nevertheless, other terms which have no purpose other than to 
deny. An alien, even within a limited universe of discourse, is 
defined entirely in terms of what he is not. A bachelor connotes 
an unmarried man, and bachelors (as bachelors) have nothing 
in common save that they are not married. Such terms are 
positive as to denotation, but negative as to connotation. But 
even these terms can, I believe, be brought under our general 
rule. The positive term as understood by common sense and 
ordinary logic is positive directly and definitely, the negative 
term is positive indirectly and indefinitely, but none the less 
genuinely. In a later chapter on immediate inference I shall 



as at any rate capable of contributing some factor to the ideal fabric of 
reality. But it assumes the external shape of ignorance, or at least of 
failure, and the paradox consists of this — that in negation the -work of 
positive knowledge appears to be performed by ignorance. The contradic- 
tion arises, as we have seen other contradictions arise, from the adoption by 
thought of a shape which at best expresses it but partially, and the reten- 
tion of that shape when the aspect which it did express has come to 
be dwarfed by other aspects of knowledge. ' ' Logic, I, 293. 



74 FOOTNOTES TO FORMAL LOGIC 

advance a new interpretation of the ancienl rule for distribu- 
tion based upon this distinction which I think answers the much 
debated question as to the validity of inversion. 

We here encounter the same problem that confronts one 
wherever one lias to do with the "relational way" of thinking. 
We begin with what appears a mere couple, a two in relation. 
Bui the "endless fission' ' breaks out and we discover that no 
relation is purely diadic. Relations are ahvays within as well as 
hi twi i n : and while they are explicitly diadic they are implicitly 
triadic. In earlier paragraphs we saw this to be true of the 
relation between form and matter, denotation and connotation, 
intension and extension. They are all correlatives having inde- 
pendent variability within some larger wiiole. Now this con- 
ception of the essential triadic character of every relation pro- 
vides an explanation, I believe, for the class of bare denials 
which the relation of affirmation to denial requires. Every 
object denotes a this or a that, and connotes thisness and that- 
ness. Now when a this goes beyond itself for its connotation 
and accepts thatness for its meaning, we have — stated most 
abstractly — a pure negation, a bare denial. And such abstract 
statement of the problem I venture to think is not a mental 
''fiction." We have thus properly provided for the outstand- 
ing "rare" cases where the mind halts between denial and 
affirmation. 

All of this suggests, as Windelband and Kant before him, 
have held, that there is a third kind of quality between affirma- 
tion and negation, and in a sense coordinate with them. Where 
there is no sufficient positive ground for a direct assertion the 
mind is satisfied with probable, indirect or negative grounds. 
But, furthermore, it should be pointed out that every indictment 
of the infinite judgment, which begins, as most criticisms do, 
with a condemnation of the negative term, is an illogical pro- 
cedure, for terms are not the prior units out of which the judg- 
ment is constructed. The judgment is itself the unit of thought 



XEGA TION AND THE IX FINITE J I WG M K V T 7.-) 

and the negative term is derived by abstraction, or dismember- 
ment of a prior infinite, or limitative judgment. We do not find 
the non-S's and the non-P's lying about ready made and then 
proceed to affirmations or denials about them. These negative 
terms are the by-products of the reverse process. We first 
observe that P cannot be attributed to 8 and state this fact in 
the negative judgment "S is not P." Whereupon the query 
arises, if P can not be attributed to S, what can be ? In answer 
to this question, non-P is created and the response is embodied 
in the pseudo-affirmative judgment "S is non-P." The nega- 
tive judgment "S is non-P" affirms something indefinite. There 
is, therefore, abundant reason to assert with Lotze that the true 
meaning of this latter judgment is never available for practical 
purposes until it is restored to the negative which was it source. 
But now it should be observed that the negative term non-P 
is not truly indefinite in the sense of being wholly undefined or 
unbounded. In the technical language of the schoolman, it is 
always distributed. And if it is genuinely distributed we do 
have some knowledge that extends over the entire class or else 
the ancient doctrine of distribution falls to the ground. To say 
that non-P is distributed is to declare emphatically that it is 
not entirely impossible to hold together the large and apparently 
chaotic group of objects comprised in non-P. The fact of dis- 
tribution declares that there is at bottom an essential homo- 
geneity in the group, and this guarantees the accuracy of all 
the transformations in which the negative term is employed 
in the various immediate inferences. Obversion, or infinita- 
tion, is for this reason a valid inference. I think no defender of 
the infinite judgment has ever claimed that non-P can exist as 
an independent concept. We can not, it is true, conceive such 
a class of objects, that is, we can form no mental picture of it. 
It is, therefore, unintelligible, but not on that account unthink- 
able. We can employ it both in the theoretical and in practical 
thought processes. The symbolic logician makes rigorous use 



FOOTNOTES TO FOBMAL Lome 
of it in his theoretical thinking, and the empirical scientist 

applies it continually ill his search for causal connections. The 

sciential narrows the field in any inquiry by destroying, one by 

one. the possibilities of his multiple hypothesis. And, as I have 
already insisted, each destruction of a possibility is a positive 
advance towards his goal. 

It is quite true that the mind is rarely ever satisfied to remain 
in the stage of hare denial, lint it is precisely these exceptional 
cases where it dot's halt at bare denial, however rare they may 
he. that logic must take into account. We may ask two questions 
here: (1) Should we at any time be unable to pass through 
bare denial to denial with affirmation, have we made no logical 
advance whatever? (2) If the infinite judgment is illogical 
and impractical, how can we explain its persistence in thought 
and language? I shall attempt to show that it is no answer 
to these questions to say with Hegel that the infinite judgment 
is "idiotic." 

The history of Logic has repeatedly taken cognizance of this 
dilemma about negation, and yet, in my opinion, there is no 
real warrant for the disparagement of the infinite judgment. 
The modern critics provide the answer to their criticisms in 
the emphasis that they place upon the difference between the 
assertion of impossibility and the denial of necessity. Absence 
of a reason for assertion, it is justly held, does not mean the 
presence of a reason for denial. To have no' opinion against, is 
not the same as to have an opinion for. It is possible, is not a 
legitimate inference from we do not know it to be impossible. 
There is some justification for the view that there is no middle 
ground between affirmation and denial — that there is no such 
thing as suspended affirmation. But now whatever position we 
take on logical the problems here in question, it is nevertheless 
an undeniable psychological fact that the mind may put itself 
in three different — even if not correlated — attitudes towards any 
suggestion. It may not only accept or reject, it may also doubt. 



XEGATIOX AXD THE INFINITE JUDGMENT 77 

At an election the counter records the "ayes'' and "noes" and 
also the "not voting." And in Psychology we are told often 
of the indifferent zone that lies between the extremes in sensa- 
tion. It is an answer not to the point to say that the state of 
consciousness called indecision is decision not to decide. The 
question is, Why do we require for Psychology and practical 
life a threefold division and for Logic a twofold division ? 

We see, therefore, that a careful examination of these con- 
siderations which seem to militate against the infinite judgment 
shows that they are unfounded. In the first place it can be 
shown that the infinite judgment, in the process of delimiting 
any universe of discourse, if not the whole objective system, has 
made a distinct forward movement. And this step does not have 
to be retraced, that is to say, a second infinite judgment in the 
next stage of division proceeds from where the first left off. It 
is not like the process of throwing a die where each throw is 
no nearer certainty than the one before it. The infinite judg- 
ment is no logical treadmill. In theory it is true, as Plato and 
after him Kant said, that the infinite judgment subtracts one 
from the infinite number of possibilities, and leaves remaining an 
infinite number. But in practice, the application of successive 
infinite judgments does very rapidly reduce the total sphere. 
Only half a dozen steps are needed in the Tree of Porphyry 
to pass from a summum genus to a very definite infima species. 
A practical illustration of the rapidity with which the successive 
infinite judgments will narrow a field of inquiry is found in 
the familiar parlor game of "twenty questions." Here one 
person undertakes to perform the apparently impossible feat 
of telling what another is thinking about by asking him twenty 
questions to be answered only by yes or no. This is often 
accomplished with surprising swiftness. 

All the so-called negative results in the experimental work 
of scientific laboratories may be expressed in each instance in 
the form of an infinite judgment; and these negative results are 



78 FOOTNOTES TO FOBMAL LOGIC 

surely not without value. The scientist assumes that the object 
o\' his search will be found in a certain field, but after laborious 
investigation discovers thai he has set up a false hypothesis, and 
must seek elsewhere for the cause of the phenomenon under 
investigation. lie registers this fact in the infinite judgment. 
"S is )io)i-r." And lie intends that the judgment shall be 
genuinely affirmative, for he knows that the phenomenon must 
have a cause. The clearing of the field by the destruction of 
false hypothesis is not idle. The scientist never hesitates to 
publish his "failures to find" for the guidance of fellow workers 
in the same field. A negative Baedecker (if one dared to print 
such a guide book) which told tourists where not to go, might 
be more useful than the positive form. It would permit of real 
discoveries by the independent seeker. 

Ill 

The symbolic logicians have pointed out the significant fact, 
that the term P is no more indefinite than the term non-P. Why 
should we think that the objects that compose the class P are 
any more homogeneous than those of the class non-P f The 
belief that one of these classes is small and homogeneous and 
the other large and heterogeneous is an idea that is thrust in 
from without. Granted that the members of the class )io)i-J } 
have nothing in common save the absence of S, this does not 
make them a less coherent group than the class P. Non-P is, 
indeed, the contradictory or negative of P, but in Formal Logic 
either of the two terms which stand in the relation of contra- 
dictories may be taken as the positive and the other as the nega- 
tive. For example, a powerful social, political or religious move- 
ment often grows from small beginnings w T hen its adherents were 
described by some negative word. The Anti-Saloon party in some 
prohibition communities is overwhelmingly large, positive and 
coherent. The fundamental fact with which Formal Logic is con- 
cerned is that the two classes /' and non-P are mutually exclusive 
and together comprise the whole universe of thinkable entities. 



NEGATION AND THE INFINITE JUDGMENT 79 

Symbolic logicians have also said that Kant's threefold 
classification of propositions into positive, negative and infinite 
has no theoretic defense ; it depends entirely upon practical 
differences of meaning. The three forms "S is P," "S is not 
P," and S is non-P have their origin not in any strict doctrine 
of negation, bnt in the practical convention of something less 
than complete negation, namely, opposition. In all those judg- 
ments in which the predicate is regarded as an attribute, it is 
for practical purposes quite sufficient to use opposites, that is, 
terms which mutually exclude each other, as do contradictories, 
but which do not together include the entire universe of think- 
able objects. The class of infinite judgments is a concession to 
contrary negation, and to the attributive view of predication. 
And this view, as I have already tried to show, is merely a neces- 
sary stage on the way to the class view of Symbolic Logic. 

It has often been maintained that the assertion of a mere 
distinction, that is, an assertion of differences in degree is no 
assertion. This is only partly true. The common definition of 
negative or contradictory terms, that they are two terms that 
are mutually exclusive and that together exhaust the entire 
universe of thinkable things, needs some qualification. They are 
totally different, the definition says, that is, different in kind. 
Now this distinction between differences in degree and differ- 
ences in kind is one which Logic has always regarded as of the 
deepest significance. But what, we may ask, is the criterion 
of this distinction between the differences in degree and the 
differences in kind? Entities which are different in kind must 
after all have something in common. They must belong to the 
same universe of thought somewhere, otherwise they would have 
ceased to be two and would have become nothing. The Hegelian 
criticism of the Aristotelian Law of Contradiction is just. 
Where there is a distinction there must be at least one principle 
of unification. Only one thing can both be and not be, namely, 
nothing. 



so FOOTNOTES TO FORMAL LOGIC 

While A and non-A are different in kind, yet it is evident 
that that which differentiates one of these conceptions from the 
other is not an intrinsic principle. There is nothing in the 
nature of the two conceptions which can tell us where the one 
ends and the other begins. The principle of this division is 
always extrinsic, that is, it lies in the purpose of the thinker. 
Every dichotomous division is made in the interest of an external 
need. Without such an extrinsic point of departure we should 
pass from .1 to non-A by imperceptible gradations within the 
same qualitative sphere. However far apart we place A and 
non-A t they will have something in common, otherwise they 
could not be thought together. The same norm that defines A 
will also define non-A. 



CHAPTER V 

The Nature of Inference 

I 

The dictionaries have found it necessary to give a score or 
more of synonyms to cover the many uses of the word inference 
by philosophers and laymen. 1 

Logicians have not been so much concerned with the ambiguity 
in the word, as with the contradictions that seem to lie at the 
heart of the process of inference itself. Aristotle, very early 
in his thinking about the fundamental problems of Logic, dis- 
covered the paradox in all judgment. No term it seems, can 
be truly predicated of another term ; it can only be predicated 
of itself. The only true propositions are the identical propositions. 
You can not truthfully affirm that "A is B," but only that 
"A is A." This dilemma arises then, in saying "A is B," you 
predicate what the object A is not, and you therefore speak 
falsely; but on the other hand, if you say "A is A/' you indeed 
predicate what it is, but you say nothing and the judgment is 
idle. So thought vibrates between the extremes of tautology 
and falsity ; apparently with no possibility of a resting place 
between the two. 

Now while the modern logicians profess to be seriously dis- 
turbed by this ancient dilemma they define inference in ways 



1 Some of the dictionary synonyms of inference are: analysis, anti- 
cipation, argument, argumentation, assay, assent, assumption, conclusion, 
conjecture, conviction, corollary, criterion, decision, deduction, demonstra- 
tion, dilemma, discovery, elench, enthymeme, examination, experiment, 
experimentation, finding, forecast, generalization, guess, hypothesis, illa- 
tion, induction, inquiry, investigation, judgment, lemma, moral, persua- 
sion, porism, prediction, prevision, presumption, probation, prognostica- 
tion, proof, ratiocination, reasoning, research, sifting, surmise, test, 
theorem, verdict. 

[81] 



B2 FOOTNOTES TO FORMAL LOGIC 

that show they have for the most part ignored the paradox. 

The conclusion in any inference, mediate or immediate, we are 
told in varying Language must he (mother, or a new, or a differ- 
ent, or a fresh proposition. Bui we find few serious attempts 
to define otherness, newness or difference. Again we are told 
that inference is the "explication of implications," or the 
■' passage from one fact to another"; it must be "more than vain 
repetition." Or it is the "supporting of a judgment by its 
reasons," the "discovery of necessary connections," "combining 
of two premises so as to cause a consequent conclusion, or "draw- 
ing a conclusion from premises." And again none of the essen- 
tial words are clearly defined. The writers often confess that 
they are employing the significant words of their definition in 
"new" ways, that the meanings that they attach to them are not 
in conformity with ordinary human usage. Hobhouse suggests 
that there is something unusual in his use of the word "new," 
by continually writing it with quotations. 

It will be well to consider several of the typical definitions 
of inference ; to show how they reveal in varying degrees the 
1 ' circle in defining. ' ' Adamson says : 

Inference is that mental operation which proceeds by combining two 
premises so as to cause a consequent conclusion. Some suppose that we 
may infer from one premise by a so-called "immediate inference." But 
one premise can only reproduce itself in another form, e.g., all men are 
some animals; therefore some animals are men. It requires the combina- 
tion of at least two premises to infer a conclusion different from both. - 

Later we shall examine this view that rejects the immediate 
inference. I wish at this time to point out that the expression 
"to cause a consequent conclusion" is ambiguous, redundant, 
and inclusive. It tells us only, at best, that an inference is an 
inference. And this circle in defining lurks in all the other defini- 
tions. According to Joseph: 



i Ency. Brit. XVI, S79. 



TEE XATUHE OF IXFEBEXCE 83 

Inference is a process of thought which, starting with one or more 
judgements, ends with another judgement made necessary by the former. 
The latter, which in relation to the judgement or judgements from which 
the process starts is called conclusion, which must in comparison with 
them be a new judgement; to repeat in fresh words our original statement 
is not inference, any more than translation is inference. For the most 
part a new judgement is only got by putting together two judgements, 
and, as it were, extracting what they yield. But there are a few con- 
clusions which we appear to draw, not from any "putting together" of 
two judgements but simply from the relation to one another by putting 
together of the terms in one judgment. This is called immediate infer- 
ence^ 

Welt oil's definition reads: "Inference or reasoning is the 
process by which we pass from affirming one or more propositions 
to another different judgment which we make as the necessary 
result of accepting the first." Also, "Conclusion states the orig- 
inal truth in a new form/' 4 And again, "Inference or reasoning 
is the deriving of one truth from another. By this is meant 
that the new judgment is accepted as true because, and in so 
far as, the validity of the judgment from which it is derived is 
accepted." 5 Bosanquet's much discussed definition is, "Mediate 
judgment or inference is the indirect reference to reality of 
differences within a universal by means of the exhibition of this 
universal in differences directly referred to reality." Miss 
Jones says, ' ' One proposition is an inference from another, or 
others, when the assertion of the former is justified by the latter 
and latter is, in some respect different from the former." 7 
Windelband insists that "Inference is nothing else than a way of 
establishing judgments, and is indeed a judgment by means of 
judgment."- This definition is satisfactory until we come to see 
that the whole question at issue is just the meaning of this 



* Introduction to Logic (Oxford, Clarendon, 1906), p. 209. 

* Manual of Logic (London, Clive, 1891), V, 24. 
•-■ Ibid., I. 256. 

« Logic, I. 4. 

" Jones, E. E. C, Elements of Logic (Edinburgh, Clarke, 1890), p. 139. 

b Ency. Philos. Sci., I, 27. 



M FOOTXOTES TO FORMAL LOGIC 

process of "establishing" judgments. Inference lias very often 
been described as the extracting from a proposition of its implied 
meanings, or the explication of implications. But here we have 
again a petitio, for this description presupposes the definition of 
explication and implication. The symbolic logicians have recogn- 
ized this inevitable circle and have for the most part frankly 
accepted among their indefinable notions the notion of impli- 
cation. 

One of the commonest of all the vagne words which we are 
tempted to employ in the definition of inference is the word 
virtually. Many writers say, that if the premise in an inference 
only virtually contains the conclusion, then, when the conclu- 
sion is "drawn from" or "extracted from" the premise, the 
"new" judgment at which we arrive will be both a different 
way of viewing and a different way of expressing the same 
truth. As a typical illustration of an account of inference which 
employs several of these ambiguous words I cite the following 
from Joseph: "In all inference there must be some movement 
of thought ; we must conclude with something not quite the same 
as what we started with ; though the obviousness of the infer- 
ence is no ground for denying that it is inference." 10 This 
activity of thought as it passes on to a "fresh" point of view, 
this step which it takes as it clothes itself in a "new" form, is 
an inference. But such an account I am inclined to think does 
not get to the center of the difficulty. It has solved the problem 
by translating it into a new form. The vital question is, What 
is the difference between a judgment that is actually and one 
that is only virtually contained in the premise? Again we may 
ask, What have we added to the "old" when we say that thought 
lias been "active" in "stepping" to the new point of view? 



» e.g. Russell says: "A definition of implication is quite impossible. 
If ji implies q, then if p is true q is true, i.e., p's truth implies g'a truth; 
also if q is false p is false, Le., q*B falsehood implies p'n falsehood. Thus 
truth and falsehood give us merely new implications, not a definition of 
implication.' 1 Principles of Mathematics, p. 14. 

10 Introduction ><> Logic, p. 217. 



TEE NATURE OF INFERENCE 85 

When is the change not a step ? It is said, that the obviousness 
of the step is no objection to calling it an inference. And again, 
we have on our hands the word obvious which is quite as vague 
as virtually, new, old or fresh. Since inference is not really a 
transition in time, it is evident that a conclusion will not lose its 
character as inference as soon as it becomes obvious. Inference 
involves discovery but it does not cease to be inference when 
(the discovery having been made) thought vindicates the infer- 
ence by proof. As Bosanquet has so well said, "Discovery ivith- 
out proof is conjecture; an element of proof is needed to con- 
stitute inference, and indeed to constitute discovery. The activ- 
ity of inference cannot be identified with the perception of 
something new. It is quite a normal occurrence that the ele- 
ments which are indirectly referred to reality should also be 
directly referred to reality. ' ni 

Hobhouse says: "Any assertion is 'new' (as compared with 
some other) as long as the two contents are in any way distinct. 
"Whatever the real inseparability of the facts, as long as they are 
distinct to pass from the one to the other is to make a new 
assertion. ' ' 12 But it seems to me that Hobhouse has not reached 
the central issue either. To define the "new" as that which is 
"in any way distinct" is hardly satisfactory. We are at once 
confronted with the difficulty of showing how two contents may 
be regarded as distinct if they have, as he declares, a real insepa- 
rability. In all his discussions of the nature of thinking, Hob- 
house has quite consistently maintained that it is the primary 
function of inference to reach "new" facts. But in the last 
analysis, by "new" facts he means those which have not been 
presented to the mind in any previous sense perception or act 
of memory. But the past is connected with the present by a 
continuous tie ; therefore predication, which always passes be- 
yond the present, can not be truly novel. Every theory of infer- 



11 Logic, II, 8. 

i 2 Hobhouse, Theory of Knowledge (London, Methuen, 1896), p. 216. 



FOOTNOTES TO FORMAL LOGIC 

ence must finally go back to the world-old Platonic Doctrine of 
Recollection, [nference is the process of discovering what we 
already logically possess but did not observe thai we possessed 
until we psychologically came upon it. 

It' consensus of opinion may be taken as a warrant for the 
assertion, the modern discussions as to the nature of inference 
have shown that it must be more than direct apprehension, or 
immediate experience. We It on says, "Inference involves 'mental 
process, 9 and with this others, for example Joseph, agree. 
They declare that in all inference there must be some "move- 
ment of thought." But here again are we not begging the whole 
question 1 How shall we decide when and in what way thought 
has moved? What is to distinguish between a mental process 
which yields an inference and that state of consciousness which 
is not a process and which is therefore characterized as bare 
tautology. I confess that often in these pages I have myself had 
to resort to the expression "movement of thought," but I have 
tried to show that these words are meaningless unless they 
involve a reciprocating process — forward and backward, analytic 
and synthetic. The paradox of inference does not disappear 
when (as some writers seem to think) we attach adjectives to 
the terms, old and new, to the inference and the inferend. We 
are told that the conclusion of an inference must not be a mere 
repetition of the old — that there must be genuine novelty. But 
this does not dissolve the paradox. Any tautology is bare 
tautology and any novelty is genuine novelty. 

The objection which Mill, and after him, Adamson and others 
have raised against the immediate inferences, namely, that there 
is in the conclusion no "new" truth, will hold also against 
mediate inferences and even against induction. The attempt to 
regard induction as different in kind from deduction breaks 
down under the weight of its own inherent self-contradiction. 
The logician who oilers a theory of induction that attempts the 
self-vindication of its own processes has on his hands this 



THE XATUEE OF INFERENCE 87 

dilemma : either he tacitly presupposes the universal truths and 
hence his method is not their sole source, or, on the other hand, 
they remain unproved because his method is confessedly a method 
of probability only. The syllogism, as was pointed out by its 
earliest critics, is indeed incompetent to supply its own premises. 
But now, when induction steps in to furnish deduction with 
these universal truths for its premises, it is shackled by the same 
fetters from which it proposes to relieve deduction. Induction 
is itself a process of reasoning from premises, and must obey the 
fundamental law which governs deduction ; the conclusion is true 
only if the premises are true. In a commendable, fraternal spirit, 
induction would remove the "mote" from its brother's eye, dis- 
regarding the "beam" in its own. The symbolic logicians are 
right, in my opinion, in their criticism of induction. 13 

II 

The dictionaries, and many of the ordinary textbooks in 
Logic have defined inference in terms of judgment and judg- 
ment in terms of inference without recognizing or confessing the 
"circle." Many attempts have been made by recent writers, to 
establish either a temporal or a logical priority in favor of one 
or the other. Such discussions have generally resulted in the 
discovery that each of these functions may be taken either as 
chronologically or logically prior to the other. In attempting 
to distinguish between judgment and inference, we find that the 
ambiguity between these two words has made it possible for one 
writer to make inference prior to judgment while another makes 
judgment prior to inference. Both judgment and inference as 



!3 Cf. Bussell, Principles of Mathematics, p. 11. "What is called induc- 
tion appears to me to be either disguised deduction or a method of mak- 
ing plausible guesses." Also Shearman, Scope of Formal Logic (London, 
1911), p. xiv. "In so far as such studies set forth methods of proof 
the studies are formal in character, and in so far as they refer to matters 
that are preliminary to the application of proof, thev are not Logic 
at all." 



FOOTNOTES TO FORMAL LOGIC 

conscious processes pass through various stages of development. 
When we take inference al its early, rudimentary and uncon- 
scious beginning, we shall find it of a lower order than judgment, 
if at the same time judgmenl is taken at the highest stage of its 
development. And on the other hand primitive judgment is 
needed as a prerequisite for overt inference. Judgment is the 
lower limit of inference and inference is the upper limit of judg- 
ment ; that is to say, in judgmenl t lie given fact, the process of 
its just itieat ion, and the product are merged into a single state- 
ment. 

Bradley has made the difference between inference and judg- 
ment depend upon the directness or indirectness of the reference 
of the predicate to reality. He has defined judgment as the 
<Unct reference of a content to reality and inference as the 
indirect reference of a content to reality. This is a distinction 
that at first sight seems very clear. But we soon discover that 
we have only postponed the difficulty and have stated the orig- 
inal question in a new 7 form. When we pursue - our analysis into 
the distinction between direct and indirect we seem soon to be 
lost in another maze of bewildering perplexities. The essence 
of Bradley's doctrine is that whenever, on the strength of w r hat 
we know about a this, we make an assertion about a that, we are 
inferring. But as we saw in a previous chapter, there is no 
distinct and intelligible line of separation betw r een the this and 
the that. The whole theory hinges again upon the distinction 
between the explicit and implicit which is not a distinction in 
the form, but only in the matter of thought. However, I believe 
the "circle" is less objectionable in Bradley's w r ay of distinguish- 
ing between judgment and inference than in any other. 

Every judgmenl when called upon to exhibit its reasons 
develops into an inference. This statement does not refer to the 
inductive process of establishing the universal propositions that 
are required for deduction. We have seen that judgment begins 
its existence when it is observed that the predicate might have 



THE NATURE OF INFERENCE 89 

been something else. Now in order to cause the judgment to 
become conscious of its reasons we have merely to hold in thought 
a suggested contradictory predicate as a substitute for the predi- 
cate actually found in the judgment. This actual predicate, in 
the process of rejecting the possible predicate, vindicates itself 
with a because. Thus the judgment "S is P" expands into the 
following disjunctive inference: "S is either P or non-P," but 
for such and such reasons "S cannot be non-P/' therefore "S is 
P." Moreover, this fact that judgment vindicates itself by 
enlarging into an inference is another way of stating the general 
idealistic doctrine that all knowledge is a system of parts so inter- 
related that the whole may be unravelled from whatever point 
we begin. 

As Hobhouse and others have said, there is no psychological 
evidence that inference is developed among the states of con- 
sciousness later than judgment, or that it in any way makes use 
of the completed process of a prior judgment. As soon as the 
object is presented to the mind it is stimulated not only to make 
an analysis of the fact itself but also to compare it, to notice its 
position in the system of facts. From simple apprehension, 
through conception and judgment, to inference, the process is 
one undivided whole. Both inference and judgment start with 
something given. Each represents a particular way that the 
mind has of reacting upon this datum. Judgment begins with 
terms which it either analyses or combines. The inference begins 
with propositions which it likewise analyses or combines. They 
differ merely in the character of the material upon which they 
operate, and consequently may be said to differ not at all, or to 
differ merely in degree. In the one case the difference between 
the datum and the conclusion is explicit and in the other it is 
more or less implicit. Although they are inseparable aspects of 
one mental fact, nevertheless explicit judgment comes into con- 
sciousness before explicit inference. Here, again, we have an 
illustration of that universal law in the evolution of thought, 



90 FOOTNOTES TO FORMAL LOGIC 

namely, thai we become aware of the concrete result or product 
first, and the process or law later. 

A casual examination of any instance of "I think'' reveals 
both a forward and a backward movement of thought. The one 
movement is from premises forward to conclusion, the other from 
conclusion back to premises or "reasons." In the former case 
we say ".!/" is P and S is 31. hence, therefore, or consequently S 
is P." This is commonly called inference. In the other we say 
"S is P" because, for or since "M is P" and "S is M." This 
is proof or demonstration. In discussing the nature of analysis 
and synthesis previously, I urged the importance of viewing 
these two movements as inseparably correlated aspects of any 
complete living thought. And again in the matter of the relation 
of inference and proof, both are always found together. There 
is never a forward movement of thought, that can know itself 
to be a genuine forward movement, if it does not always feel 
at its center its own latent backward movement. There is no 
inference — no true discovery — without proof. A discovery that 
is bereft of this validating backward movement would be pure 
adventure (if that were possible). But now, analytic attention 
to the thought process always finds one of these movements more 
prominent than the other. "We might employ the word reason 
to denote the combined forward and backward movement in its 
logical totality. Then the word inference might stand for the 
process of attaining a belief and proof for the process of sup- 
porting the belief. 

The real problem at issue in immediate inference is not the 
determination of the precise limits which any judgment places 
upon the various movements or aspects of its meaning. This is 
transformation or what Bosanquet has called "interpretative 
inference"; it is the determination of all the ways in which the 
predicate may be referred directly to the subject. "Substantial 
inference" we have when we pass from one content or relation 
to a not In-!- indirectly. It is difficult to distinguish between a 



THE XATUSE OF INFEBENCE 91 

direct aud an indirect reference to reality. The difference is 
between what we see and what we do not see, but what we might 
see from another point of view. And this is not a distinction 
that depends upon obviousness or immediacy in their ordinary 
meaning. Inference is a process which changes our power of 
perceiving the object. DeMorgan remarks that "inference does 
not give us more than there was there before, but it may make 
us see more than we saw before." The perfect mind makes no 
distinction between direct and indirect reference to reality. It 
is not obliged to say, "The facts present are thus and thus, 
therefore I should infer that facts not present are thus and 
thus. (Omniscience does not have to compare facts in order to 
know them.) It has what might be called a unito-multiple point 
of view, from which the difference between the direct and the 
indirect insight disappears. It does not have to run around an 
object to see how it looks on the other side ; it sees both sides at 
once. 

Ill 

The attacks on Formal Logic invariably proceed upon a mis- 
taken understanding of the manner in which the idealist thinks 
of the relation between form and matter. Since Hegel, many 
logicians have reaffirmed his doctrine of the essential correlativ- 
ity of these two aspects of reality. We have come to see that 
form and matter do not exist separately, nor can they even be 
considered entirely apart from each other. We should not think 
of them as we think of the seal and the wax in the classic illus- 
tration of form and matter. And yet we may speak of the form 
of reasoning as being different from its matter, without con- 
tradiction. In truth, while there is no final and complete sepa- 
ration of matter from form, there is yet a difference amounting 
to a relative distinction. Although the two are not a separated 
twain, they are nevertheless separable. They are, in fact, inde- 
pendent variables within their correlation. The mathematician 



92 FOOTNOTES TO FORMAL LOGIC 

lias to deal often with such binary systems of independent 
variables. In the world of sensory facts, too, we frequently find 
one ami the same form encompassing a variety of contents at 
different times and places, and on the other hand, the same con- 
tent manifests itself in a variety of forms. Moreover the inde- 
pendent variability goes so far, paradoxical as it may seem, as to 
permit the one to pass into the other. "What is form in one rela- 
tion becomes matter in another relation. This latter truth is 
of the greatest importance for the right understanding of the 
theory of thought that in current discussion calls itself dynamic 
idealism. 

The serious question for Formal Logic is whether, in this 
eon-elation, we can ever escape the necessity of defining each by 
the other. There are many such circular definitions; for 
example, form is that which remains permanent when the matter 
changes and matter is that which remains permanent when form 
changes. It has often been remarked that all reasoning is in the 
last analysis circular, that no definition can escape the indict- 
ment of begging the question. But whatever position one may 
take on the vexed question as to the possibility of transcending 
reciprocal relations in definition and description, we may yet 
maintain that thought itself does pass from thesis to antithesis 
and thence to synthesis, although language may lag behind. The 
third stage of genuine synthesis, that is, the synthesis that does 
not itself in tnrn require an antithesis, must elude logical defini- 
tion. Here it may be said is an instance of a judgment that has 
no exact counterpart in the realm of propositions; vocabulary 
has not followed thought. Now the thought which reconciles 
the contrasting correlation of form and matter can only be 
described by again employing the word, form. The Real Logic — 
the contemned Logic iiberhaupt — would be concerned with this 
form. This is what idealism has always meant by the synthesis 
of opposites in higher unities. It has not meant, for example, 
that good is had, or thai past is present, etc., but that these 



THE X ATV HE OF INFERENCE 93 

correlatives have something in common. In like manner there 
must be something in common between the form and matter of 
thought. 14 But it must not be supposed that we are here reaffirm- 
ing the very old view that the form is always the constant and 
the matter the changing characteristic. As I have just said the 
form may change and the matter remain fixed, or the matter may 
change and the form remain fixed, or finally both form and mat- 
ter may vary. A wave, for instance, at no two moments of its 
life history has either the same form or the same content. Yet 
the wave unquestionably has an identity that persists amidst its 
changing form and matter. It is an individual because it is the 
object of a will-attitude. 

Since the time of the great Stagirite, logic has been looked at 
under two aspects: (1) real logic, (2) formal logic. Both of 
these expressions are full of ambiguities — ambiguities that are, 
however, hardly avoidable. Real Logic deals with the problem 
of correspondence, Formal Logic with the problem of consistency. 
The truth of correspondence joined with the truth of consistency 
constitute total reasonableness. The question at issue is whether 
these two aspects enter into total reasonableness in different 
degrees of importance. Can the question of coherence be 
divorced from the question of correspondence? Is correspond- 
ence, at last, a kind of coherence? These two main senses in 
which we may speak of the validity of thought, have been the 
pivotal points around which the recent discussions regarding the 
nature of inference have revolved. The Instrumental Logic of 
today denies that there are these two aspects ; it dispenses entirely 
with the ontological problem. Idealism has always insisted on 



14 Windelband has clearly recognized the necessity of distinguishing 
between these two points of view. ' ' The two kinds of categories may be 
distinguished as transcendent and immanent in their relation to truth; so 
that I would say that the constitutive categories are existential and the 
reflective are valid. It is the final task of the system of categories to 
reunite the two divided sories and to discover the forms of thought in which 
the two fundamental categories, the valid and the existential, are eombined 
into a unity." Enry. Philos. Sd., I, 35. 



i)4 / 00TN0TE8 TO FORMAL LOGIC 

the distinction between the ontological and the epistemological 
problem, even when (as in the case of Hegel) it asserts that 
Denkenlehn ist audi Seinlehre. It declares thai the relation of 

thought to reality is a real problem, and thai the recent attempts 

to solve it by Baying thai there is no such problem or by asserting 
that it is of no consequence, is a profound error 

The question, ''Is this particular instance of reasoning 

accurate?' 1 is at heart, always a duplex question. Although for 
practical purposes we may ignore one or the other of these two 
aspects, rigorous thought demands that we make the distinction. 
We may have had in mind to ask whether the inference is itself 
a manner of Being — whether we have laid hold of the real nature 
of things through this mental operation. In the second aspect 
of the duplex question, we disregard coincidence with reality 
entirely; we wish merely to know if our conclusion does follow 
from the premises in accordance with non-contradictory princi- 
ples. In the face of all these recent indictments we still declare 
that Formal Logic is the science of that part of reason which 
is concerned not with total reality and complete reasonableness 
but with the truth which is contained in consistency. Consist- 
ency is a part of truth, necessarily, but it is only a minor part. 
The form of thought is unanalyzable and indefinable. The 
best we can say of it is that it is the mode or manner in which 
thought is. It is not an external matrix, independent of thought, 
but is natural to thought. It is intrinsic in the nature of thought 
itself, and in so far it is an expression of that nature. But it is 
not a complete expression, any more than the form of a statue 
is a complete expression of the statue. It is, however, a genuine 
expression of the inner life of thought; an expression that is 
spontaneously taken by thought. To say that thought is deter- 
mined by this form is inaccurate and insufficient. What we 
mean to say is that thought is self-determining in its form. The 
form of thought is essential to thought, though not equivalent to 
tie- fulness of thought : thought does not subsist without thought- 






TEE X AT FEE OF IXFEEEXCE 95 

form. Thought, as thought, has this form, and without it thought 
in so far is non-existent. The form of thought is peculiar and 
untranslatable. Serious misunderstanding has arisen from the 
''wax and seal" illustration of matter and form of thought. It 
would be well if this and all other similar figures of speech 
could be expunged from logical discussions. These similes are 
largely responsible for confusion of logical form with temporal 
sequence or spatial arrangement. 

Furthermore, logical form is not the same as that something 
in objects that we call the beautiful nor is it that other some- 
thing in objects that we call the good. "We cannot escape the 
conclusion that there exist in consciousness more than one prin- 
ciple of arrangement. But this admission must not be regarded 
an abandonment of our defense of Formal Logic. The elements 
in a certain sort of consciousness are arranged in a particular 
way, while the elements in another sort of consciousness are 
arranged in another way. We have the time-principle, and the 
space-principle, both existing and acting together in conscious- 
ness. Also we have the esthetic and the moral principle. Things 
may be satisfactorily arranged in regard to time and space, but 
yet not be beautiful ; or they be harmonious as regards the 
esthetic principle, and still be lacking in goodness. 

But there is yet another principle that we must add to the 
foregoing list. Between the time and the space principle on the 
one hand, and the esthetic and the moral principle on the other, 
comes the truth principle, and it this principle with which 
Formal Logic is concerned. Thus we get the whole series of the 
five principles of estimate, in which series the logic-principle is 
the third. There are two aspects to this third principle : in its 
highest aspect, the logical principle is that of truth absolute and 
entire; in its other aspect it is susceptible of degree. It is not 
in contradiction to what I have asserted elsewhere to say that 
the principle of reality or truth has degree : that a state of judg- 
ment may be on the way to the goal of complete truth and per- 



!><; FOOTNOTES TO FORMAL LOGIC 

feet reality, just as a thing may be on the way to the goal of 
beauty or of goodness. 

The new positivism which postulates a world of independent 
objects — brute fads — rests back upon an unwarranted abstrac- 
tion. It has taken this fundamental relation between form and 
matter and pressed the con-elation to the point of breaking. 
The matter of thought is something that is finally foreign or 
indifferent to its form. This indifference constitutes its inde- 
pendence, since that aspect of thought which is indifferent to a 
changing aspect, it would appear, cannot be otherwise than inde- 
pendent. The fallacy in this reasoning, is due to a false analogy. 
In the physical world, matter does lie in the form, like the 
pudding in the mould. But the form of thought is not something 
that is laid over the matter nor is the matter anything injected 
into the form. The form is only the class of relations in which 
flu essential nature of matter may stand. The systematic view 
of the ways in which its inner relations may express themselves is 
thought's form. 

It is unfair to the Traditional Logic to say that it has divorced 
form from matter, that it has not held form in abeyance and 
obliged it to wait upon matter. No one has been more explicit 
on this point than Bosanquet who says, "We cannot and must 
not exclude from the form of knowledge its modifications accord- 
ing to 'matter' and its nature as existing only in 'matter.' " 1,r ' 
Again Joseph has said : ' ' The form and content of thought are 
not capable of separate consideration, like the mould and the 
pudding; what from one point of view is form is from another 
[natter, and the same form in different kinds of content is not 
altogether the same, any more than is the same genus in different 

Sprcirs.'*"'' 

It is often believed that any successful indictment of the 
syllogism will carry with it the condemnation of Formal Logic, 



is "Essentials of Logic, p. 50. 
u Introduction to Logic, p. 214. 



THE XATUEE OF INFERENCE 97 

as a whole. But this does not follow. The two doctrines are not 
so interdependent that they must stand or fall together. We 
may, with Bradley, deny the univerality of the syllogism, and 
still hold that "all reasoning is formal and is valid solely by 
virtue of its form." Every inference belongs to a class. It 
has its own type, and it moves in accordance with a principle that 
governs not only it, but all other members of its class. Bradley 
is quite sure, however, that we can never determine the class of 
all such classes. 17 But this denial that there is a universal form 
of thought is itself just the final type for which we are looking. 
I confess that I see no other than the familiar traditional answer 
to this difficulty. The agnostic who says there are no final formal 
principles is asserting that there is at least one such principle, 
namely, the principle that declares that there are no principles. 
It is alleged that we cannot understand fully the essential 
nature of the thinking process if we operate merely with symbols. 
The form of thought is vitally affected by that which is thought 
about. But the opponents of Formal Logic ignore a distinction 
that is of very ancient origin, namely, the distinction between the 
two kinds of assertion that we may make. We either assert a 
relation between things (or the attributes or condition of things), 
or else we assert a relation between assertions. This distinction 
between material implication and formal implication furnishes 
the incontestable basis for Symbolic Logic. The calculus of 
propositions — formal implication — is a study that may be pur- 
sued independently of any other implication. 

IV 

Many of the attempts that have been made to reconcile the 
empirical and the idealistic theories of the relation between the 



i" Principles of Logic, p. 471. "No possible logic can supply us with 
schemes of inference. You may have classes and kinds and examples of 
reasoning, but you can not have a set of exhaustive types. The conclusion 
refuses simply to fill up the blanks you have supplied." 



FOOTNOTES TO FORMAL LOGIC 
universal and the particular in thought have been reconciliations 

in name only. They have generally allowed the opposing theories 
to make assertions that are Logically contradictory. And when 
the pacifier happens to be one of the contesting parties, the recon- 
ciliation that is effected involves the annihilation of his opponent. 
Bu1 also, equally unsatisfactory has been the reconciliation when 
the third, or benevolent neutral party, has stepped in. He has 
generally cancelled all the outstanding differences between them, 
and left the two theories standing "harmoniously" side by side 
in the night of thought in which all cows are gray. Obviously the 
idealist ma}' accept no terms of peace which would deprive reason- 
ing of its universal character. Nor may the empiricist abandon 
his own central contention that all reasoning is from particular 
to particular. The empiricist begins with the sense-presented 
particular, and proceeds thence in quest of the universal. Failing, 
however, to reach this goal by the way of the accumulation of 
particulars — the only pathway he recognizes — he boldly declares 
that the universal (even if it could be reached) would not be 
needed. All reasoning is from particular to particular, the 
universal is a convenience not a necessity. 

The relation between the particulars and the universal may 
be read off in three ways. We may read it (1) from particular 
to universal, (2) from universal to particular, or (3) from par- 
ticular to particular. It would seem therefore that there must 
be as many different kinds of thinking as there are possible 
relations here. Now Aristotle did clearly recognize this three- 
fold relationship and on the basis of these distinctions declare 
that there were three kinds of thinking. Reasoning from par- 
ticular t<» particular he called TrapaSeLj/xa. reasoning from par- 
ticular to universal eiraycovrj , and finally reasoning from 
universal to particular. avWoyia/jio^. But Aristotle was not will- 
ing to give to each of these types an independent or coordinate 
function in knowledge. Although he recognized the importance 
of analogy and induction, he was firmly convinced that these 



THE X ATE BE OF IXEEEEXCE 99 

were merely operations subsidiary to real thinking which in the 
last analysis was always syllogistic. Professor Adamson and 
others have accepted Aristotle's threefold relationship but have 
set up three independent types of inference : namely, ( 1 ) from 
particular to particular, analogical inference; (2) from par- 
ticular to universal, inductive inference; (3) from universal to 
particular, deductive or syllogistic inference. But I shall insist 
that each of these types of reasoning expresses only in a partial 
and one-directional way the reciprocating thought process that is 
at the basis of all three. 

Adamson 1 8 has maintained that all inference is mediate. But 
in setting up these three types of reasoning he has apparently 
denied the necessity of mediation. In his account, each form 
of thinking deals with two terms only. But on closer examina- 
tion we find that each of these binary relations, from particular 
to universal, from universal to particular, from particular to 
particular, has in reality a suppressed third term. When this 
third term is properly supplied in each instance we discover that 
the three forms of reasoning are really at bottom the same. Xo 
reasoning is merely from particular to universal, nor from 
universal to particular, nor from particular to particular. But 
in any complete act of reasoning we are always passing from 
particular to particular via the universal. 19 This pervading 
identity is to be sure not always nor often overtly operative; 
therefore by the popular mind and in some systems of philosophy 
it is declared to be totally absent. Wherever there appears to 
be inference from particular to particular it is because we do not 
take the trouble to state the ground, either because, on the one 



18 "We may proceed either directly from particular to particular by 
analogical inference, or indirectly from particular through universal to 
particular by an inductive-deductive inference which might be called 
'perduction. ; On the whole, then, analogical, inductive and deductive 
inferences are not the same but three similar and closely connected 
processes." Ency. Brit., XVI, 880. 

is Cf. Bosanquet, Logic, II, 30. "The conception of inference from 
particulars to particulars is thus an illusion arising from the activity in 
inference of presupposed, superficial, or unanalysed universals. " 



LOO FOOTNOTES TO FORMAL LOCK' 

hand, it is so manifest or for the opposite reason, because it is 
not immediately in view. 

Consciousness is at first neither of a particular seen as a par- 
ticular, nor of a universal seen as a universal. It is rather an 
indistinct blending of the two. Succeeding pulsations of con- 
sciousness are required to differentiate this confused primitive 
perception into one or the other. Our earliest sense experiences 
are definitely situated in space and in time. Every perception 
is present here and now. and furthermore has its causal explana- 
tion. This would seem to bestow on it individuality, but neither 
space nor time are real principles of individualism. If spatial 
and temporal relations were the only distinguishing character- 
istics, we should never be able to declare that the object of a 
present perception had not been seen elsewhere or at another 
time. The perception of the individual or the universal as such 
is impossible. They are differentiated aspects of a dual act of 
consciousness. This two-edged act of consciousness is on one 
side the discovery of certain attributes as uniquely characteristic 
of one object and other attributes as common to many objects. 
The particulars with which the empiricist deals are not really 
particulars, they are the differences in which the universal has 
exhibited itself. 

Thought, then, always operates by means of a universal. 
Furthermore, we do not think unless in knowing the part we do 
also in a sense know the whole. All of our previous and sub- 
sequent discussion turns upon this principle. Reasoning is never 
from particular to particular. There is no thoroughfare from 
one fact to another fact, except by the way of the universal. It 
is true that in the psychological analysis of the process we cannot 
discern the ascent to the universal nor the descent from the uni- 
v. isal. We see only an apparent transition directly from par- 
ticular to particular. But the logical analysis always discovers 
the necessity of tie- universal. Reasoning can not possibly take 
place unhss there is a universal within which the particulars, 



THE NATURE OF INFERENCE 101 

between which thought takes place, are embraced. If each 
so-called particular were locked up within the narrow limits of 
its own specific constitution, it would be idle to talk about pass- 
ing from one such particular to another. Yet this is the assump- 
tion from which every form of associational theory of thought 
sets out. Each idea reproduces in the content of another idea, 
not only itself, but in some mysterious way produces also the 
connecting link between itself and that other idea. 

Furthermore, it can be shown that the empiricist is deluded 
in his belief that he can make an assertion that is absolutely 
particular. No judgment has ever for its subject-matter just 
bare concrete fact. A particular judgment would be no judg- 
ment, because as Bradley has said, the subject would be "com- 
pletely shut up and confined in the predicate." Such a judg- 
ment might almost be said to be a stage prior to bare tautology, 
it would tell us nothing else about the subject or predicate than 
that each is just what it is. 

We may, therefore, deny Mill's contention that "the child 
who having burnt his fingers, avoids thrusting them again into 
the fire, has reasoned or inferred, though he never thought of the 
general maxim, fire burns." When the child avoids thrusting 
his fingers into the second fire, what warns it away is not the 
sight of the second fire, as a bare isolated particular. If there 
were no more to this second fire than just its bare identical self, 
the child would, of course, put its fingers into the flame and be 
burned again. But the second fire is something more than just 
a particular, it has something over and above its thisness. That 
from which the child withdraws its fingers is in reality the first 
fire, which it sees, by memory, in the second fire. If it should 
put its finger into the second fire and be burned, we should chide 
it with "You didn't think," which for the purpose of the defense 
of the universal, I concede is equivalent to "You didn't remem- 
ber." We avoid the issue when we describe reasoning as a 
passage from particular to particular, and blink at the universal 



102 FOOTNOTES TO FORMAL LOGIC 

which stares at us from behind the WOllld-be particular. The 
object o\' knowledge is never a pure this, it always has a fringe 

Of Ihdhh SS. 

Mill and the later-day associationists have said that ''what 
justities the transition from one particular to another is the 
resemblance between the two particulars." "We reason by means 
of the qualities which the two have in common. But this recogni- 
tion, in the second particular, of the attributes which had pre- 
viously been found in the first, is the tacit admission of the 
universal for which we are contending. In the actual thought of 
the moment we may not consciously distinguish the universal 
from the concrete instance in which it is manifested. Never- 
theless, subsequent reflection discovers that the general idea is 
always there and constitutes the only bridge by means of which 
we can reason from particular to particular. 20 



20 Cf. Bradley, Principles of Logic, p. 36. "It is not true that par- 
ticular images are ever associated. It is not true that among lower 
animals universal ideas are never used. What is never used is a par- 
ticular idea, and, as for association, nothing ever is associated without 
in the process being shorn of particularity." 



CHAPTER VI 

IMMEDIATE INFERENCE 

I 

Before considering the question of the validity of immediate 
inference, I wish to offer a revision of the names for the entire 
system of the so-called immediate inferences. Assuming that 
objects corresponding, to S and P do exist, and furthermore that 
these classes do not exhaust the entire universe, then the various 
relations in the universal affirmative proposition "All 8 is P," 
may be illustrated by the following diagram. The objections to 
"Euler's circles" have now been presented over-many times. 
No one who has ever taught elementary logic is unmindful that 
the circle notation is incompetent to express properly the rela- 
tion between species and genus. The genus is not a class that is 
divided up into sections called species. Euler's diagrams we 
all know apply only to the static relations of inclusion and exclu- 
sion. They are of service only in the calculus of classes and their 
utility is entirely illustrative. They give no truths which could 
not have been secured without their assistance. But they are of 
the highest service to students in elementary logic for the proper 
understanding of the relations within the sphere where they are 
applicable. 

These relations between two classes and their negatives have 
long been recognized and several different ways of naming them 
have been suggested. In presenting this subject to elementary 
students it is certainly conducive to clarity to have one name 
stand for one only of these relations, and to have each of the 
relations designated by a single term. In the majority of the 
systems of the names so far offered, this has not always been 

[103] 



104 



FOOTNOTES TO FORMAL LOGIC 



observed. The most of the names which 1 have proposed have 
already been employed by differenl writers, but I am not aware 
thai any one lias offered just this arrangement. If all of these 
relations had now for the first time been discovered simultane- 
ously, and a committee of philologists and Logicians were sel the 



A 




Oppositive § 




Contrapositive 




task of naming them, doubtless words derived from vrrto would 
be used throughout, and probably some attempt would be made 
to employ in each instance a word more or less suggestive of the 
relations involved. I know of only one attempt to construct such 
a simple and uniform terminology — that of Miss Jones. 1 

A most radical departure was proposed by Miss Jones, in 
substituting reversi for converse. If as I have said, these rela- 



i l-.h nu nts "i Loan-, p. 14:;. 



IMMEDIATE INFEBENCE 105 

tions were named de novo, probably Miss Jones' suggestions 
would be adopted. Reverse does suggest better than converse 
the process of reading a proposition off from its predicate end. 
But the two names converse and contra positive have been sanc- 
tioned now by so many generations of usage that it \vould be 
well-nigh impossible to make such a change. No one, so far as 
I am aware, has adopted Miss Jones' suggestion. For these two 
fundamental relations I have therefore accepted the names of 
established usage. Each of the other names which I have assigned 
to the various relations I have found employed by some writer, 
with the exception of oppositive. In Keynes 2 admirable classi- 
fication and naming of the immediate inferences, which has 
been followed by Creighton and others, some of the relations have 
compound designations, as obvcrtecl converse, partial contraposi- 
tive, etc. Other writers have employed long and awkward expres- 
sions for some of the relations, for example, "immediate infer- 
ence by privative conception" — the name given to the obverse 
by Jevons. 

It would be interesting to ask which of these immediate infer- 
ences the mind passes to first. The ordinary view is that, from 
the original we step first either to the converse or the obverse and 
proceed thence by successive obversions and conversions to the 
others. But if these other relations are all immediate inferences 
we should be able to pass directly to them from the original. If, 
however, there are two or more pulsations of thought in passing 
out to the more remote inferences they ought not to be called 
immediate. In discussing the nature of judgment I have already 
contended that all thought is in a sense mediate, that every judg- 
ment is in the end an enthymeme. If the original proposition is 
an abbreviated syllogism, and if each of the inferences is like- 
wise an enthymeme, then the true explanation of the entire sys- 
tem of immediate inferences will be found in the fundamental 
conception of the syllogism which I shall propose later, namely, 



Formal Logic, p. 140. 



L06 FOOTNOTES TO FORMAL LOGIC 

thought manifesting itself through the threefold relation of 
genus, species, and particular. The immediacy of the so-called 
immediate inferences is psychological not logical. 

Objections have been raised to all such extensions of Euler's 
diagrams, 'rinse criticisms are for the most part based on the 
existential import in the original proposition. It has been main- 
tained by Venn 8 and other symbolic logicians that the two 
assumptions that we have made concerning the original propo- 
sition are unwarranted. The proposition from which we start 
it is said, tells us neither (1) that 8 and P exist, nor (2) that 
non-8 and non-P exist. But I think this is not a serious objec- 
tion. Any explanation of immediate or mediate inferences is 
confront ihI always with the fact of a multiple hypothesis con- 
cerning existence, quantity and quality. We simply contend that 
the operation of inference here involved is unconcerned with 
these hypotheses. The process can carry along several hypo- 
theses as well as one ; it accepts what is given it and passes it 
along, unchanged, into the conclusion. This process of carrying 
along a multiple hypothesis we shall find best illustrated in the 
case of inversion — the most criticized of all the immediate infer- 
ences. Venn has objected to the hypotheses of the Eulerian nota- 
tion because they are very remote from the popular view. Formal 
Logic, however, should not concern itself with the popular view, 
but with the actual facts. All teachers of the subject bear testi- 
mony to the fact that elementary students accept easily the 
assumption of the existence of S and P and their negatives; it is 
the assertion that one or more of these classes may be non-existent 
that comes as a surprise. 



• <•(■. Venn, Symbolic Logic, (ed. 2, London, Macmillan, 1894), p. 154. 
"Prom 'All X is ST' we are commonly allowed to derive 'All not-Y is 
Not-X.' But this being a universal affirmative must indicate that there 
are instances of not-Y and not-X, as well as of Y and X. This is cer- 
tainly very remote from the popular view, which never thinks of insisting 
that X and V must not only exist but must also abstain from comprising 
all existence. " 



IMMEDIATE INFERENCE 107 

II 

In a previous chapter we saw that the several definitions of 
inference which were examined seemed all to be circular ; nor was 
our own definition free from the suspicion of a return to itself. 
In fact we accepted the circle in defining as by no means a 
calamity. There are no ultimately simple units, or points, for 
thought. It begins with circles, but circles whose radii are zero, 
so to speak — whose elements are concomitants, not sequents. We 
shall find the same difficulty confronting us when now we come 
to look more closely into the nature of the so-called immediate 
inferences. 

Every proposition has a meaning, often several; and these 
meanings have meanings. I have already spoken >of these direct 
and indirect meanings as first and second intensions of proposi- 
tions. I employ these expressions, first and second intensions, in 
quite the same sense as the scholastic usage. In the scholastic 
terminology, the first intension is a judgment about a thing, and 
the second intension a judgment about a judgment. Now the de- 
bated question whether the immediate inferences of ordinary logic 
are real inferences or just interpretations, transformations, or 
to use another suggestive expression, alternate readings, depends 
on whether we can establish any real distinction between the 
first and second intensions, the direct and the indirect meanings 
of propositions. The defense of Formal Logic depends upon the 
validity of this distinction. If the second intensions are wholly 
dependent upon the first intensions — if they have no domain 
within which they may vary independently of the first inten- 
sion — then the distinction between formal reasoning and material 
reasoning breaks down. However, if such a distinction can be 
made out, we shall be able to say that any movement of thought 
in which we pass merely from one direct meaning to another 
direct meaning, is only an alternate reading ; whereas if thought 
passed from a direct to an indirect meaning we should have a 
true inference. Perhaps this distinction has already been in 



L08 KO0TNOTE8 VO t'OUMAL LOGIC 

tin- minds of those authors of elementary textbooks who have 
distinguished betweeu implied and inferred judgments. But I 
believe the distinction in kind, upon which I am here insisting, 
can be described with a higher degree of accuracy by the terms 

direct and indirect than by implied and inferred, or actual and 
virtual. I have already tried to point oul the failure of all those 
definitions of inference which rely upon the pseudo-distinction 
between the old and the new, or that attempt to describe infer- 
ence as progress of thought, without pointing out the necessity 
of both identity and difference, action and reaction, in short, 
genuine reciprocity. As an illustration of such a definition I 
quote from Davis: 4 

An implied judgment is one that actually exists together with the 
given judgment, either merely in thought or involved covertly in the 
expression. An inferred judgment is one that only virtually or poten- 
tially exists in the given judgment, and is derived from it. The statement 
of the one is nothing new; there is no advance, no progress of thought, 
but only its full expression; that of the other contains something new, 
there is a step forward, a progress of thought. In the inferred judgment 
there is always either a different subject, or a different predicate, from 
that of the premise, and perhaps both. 

It seems unwise 1 to use the terms implied and inferred to describe 
the different moments in thought, since so many writers on 
Symbolic Logic use implication and inference as synonyms, or 
nearly so. And do not all such expressions as "step forward" 
or "covertly involved" themselves covertly involve the whole 
problem that we are attempting to solve? I am of course fully 
aware that the terms, first and second intensions, or direct and 
indirect meanings, are by no means free from the objection I 
have raised against the other terminology. 

It is quite impossible, I think, to distinguish between imme- 
diate and mediate inference on the ground of a numerical differ- 
ence in the elements involved in the process. This is the most 
ancient of all the distinctions. But when we assert that in an 
immediate inference the conclusion is derived from one premise 



i Theory oj Thought (New York, Barper, 1878), p. 10.'}. 



I Mil EDI ATE INFERENCE 109 

alone, we have substituted one difficulty for another. The vital 
point at issue is just the question as to what constitutes one 
proposition. If the oneness of the judgment in the mind is 
always to be found in the oneness of the spoken or printed 
proposition then Logic is truly just another name for Grammar. 
And this is, in fact, what some philologists claim. Logic, they 
say, being compelled to wait upon language, is entirely at the 
mercy of the accidents of speech. This obviously revives the 
old question so prominent in the writings of Hamilton, Mill, 
Mansel and Whately, whether Logic deals with language, thought 
or things. Here, as I have remarked in an earlier chapter, is 
where the doctrine of the quantification of the predicate has its 
strong hold, for that doctrine is precisely such a scheme for filling 
out the shortcomings of language. Were it not for the inertia of 
our human nature, which in language, as elsewhere, follows the 
line of least resistance, the expression of thought would be ade- 
quate to thought itself, and there would probably be no such thing 
as inference. When one goes into an East Side restaurant and 
hears the waiter call out an order, ' ' Hot cakes and ' ' — or, ' ' Ham 
and," one has an illustration of the economy of language. In 
the mind of the cook in the adjoining kitchen one would find 
the inference. However, the risk is taken, we economize effort 
and say less than we think. But we pay the penalty for the 
indolence of language in the perpetual necessity of making good 
the omissions by the process that we call inference. All efforts 
to reduce Logic to Grammar have their origin in the failure to 
observe this distinction, which I have already urged, between 
the interpretation of a proposition and the deduction of infer- 
( nces from a judgment. 

To use a mathematical metaphor, which I admit is somewhat 
riskful, we may say that there is both a one-dimensional and 
two dimensional thought. One dimensional thought is repre- 
sented by the Aristotelian system of propositions with unquali- 
fied predicates. Two-dimensional thought is represented in the 
Hamiltonian system of propositions with quantified predicates. 



no FOOTNOTES TO FOBMAL LOGIC 

For example, in the universal affirmative proposition "All 8 is 
/'" in the one-dimensional system of thought we are told of one 
relation which the predicate has. In this system when the predi- 
cate attaches itself to the subject it reserves the privilege of 
ether attachments with which 8 is not concerned. Situations 
mighl arise in which 8 would be justified in knowing P's other 
attachments, and with such situations only the system of propo- 
sitions with quantified predicates would be competent to deal. 
[f we regard the subject in extension and the predicate in inten- 
sion, "All 8 is P" means that the objects in the class 8 all have 
the attribute P; but the proposition does not tell us, and we have 
no right nor need to know whether P is an attribute of any 
other object. P could be faithful to every requirement of a 
qualifier of S and qualify other objects also. The question as to 
what else, if anything, P does qualify is a perfectly proper ques- 
tion, but this lies in a second dimension of thought. The query 
arises "where or what is 8?" and the answer is "All 8 is P." 
Then a second query arises "where or what is Pf" This is 
answered by the Hamiltonian A or U. But now it should be 
noted that the second question does not arise simultaneously with 
the first ; it is suggested by the answer to the first. The fact that 
language has rarely provided the Hamiltonian forms, shows 
clearly that the one-dimensional Aristotelian forms are entirely 
adequate to the first questions. Now I believe this distinction 
between first and second questions has an important bearing 
on the question of the validity of immediate inference. An 
immediate inference always involves the transition from the one- 
dimensional system to the two-dimensional system. The only 
genuine inference, therefore, is one in which thought passes 
from a categorical to a problematic proposition. 



b Bradley, Principles of Logic, p. 390. "The truth is that, if you keep 
to categorical affirmatives, your conversion or opposition is not rational, 
but is simply grammatical. The one conversion which is real inference 
18 ,-i modal con version, and that presupposes a hypothetical character 
in the original judgment. M 



IMMEDIATE INFERENCE 111 

III 

As we have already had frequent occasion to remark, most 
definitions say that an inference is immediate, not because it is 
obvious or direct, or is grasped in a single beat of consciousness ; 
it is immediate no matter how many so-called steps are required 
to reach it. provided no other information is used than what 
was given in the one original proposition. The immediate infer- 
ences have been so denominated because thought seems to pass 
from one judgment to another without the assistance of a middle 
term. But this conventional distinction between mediate and 
immediate inference is sadly defective in fundamental insight. 
A common ground is required quite as much in immediate as 
in mediate inference, as a means of bridging the gap between 
the two judgments. We pass from one particular judgment 
to another particular judgment only because both are embedded 
in a universal. All thought is from particular to particular via 
the universal ; and moreover the certainty and value of the con- 
clusion in any form of reasoning — immediate or mediate — 
depends upon the grip we have upon the universal. 

The logician therefore has to contend with this embarrassing 
fact that propositions, as men use them, are not always univocal. 
It is this ancient question of the precise determination of what 
is implied in a proposition, and what is extraneous matter, that 
is the cause of the difficulty which so many recent writers find 
in these transformations of propositions which have now so long 
been called immediate inferences. It is evident that, when one 
of these ambiguous propositions is given to the logician to 
operate upon, he must insist that you shall announce beforehand 
in which one of the several meanings he is to take the proposi- 
tion. However, this task of determining the precise meanings 
of propositions belongs to the person who announces it — to the 
rhetorician or grammarian. If he does not fix the meaning, the 
logician must not be blamed for drawing his inference from the 



L12 FOOTNOTES TO FORMAL LOGIC 

proposition in the form of hypothetical alternatives correspond- 
ing to the alternatives implied in the original proposition. It 
sometimes happens, however, thai even where the proposition 

from which we start seems unambiguous and categorical we can 
not infer a truth equally unambiguous and categorical. This is 
said to be the case with the relation which has commonly been 
called inversion. The inverse may be defined as "a proposition 
having the negative of the original proposition for its subject 
and the original predicate for its predicate." The inverse of 
"All 8 is P" is "Some non-8 is not P." The inverse has also 
been confused with the contra/positive, and I need only refer to 
the many other special uses of the word in algebra, geometry, 
mechanics, music, etc. 

The opponents of immediate inference have attacked inver- 
sion as, in their opinion, the weakest place in the system of imme- 
diate inferences. But I submit that no logician of repute has 
ever claimed universal categorical validity for the process of 
inversion. Keynes, who was the first to give a thorough treat- 
ment of this subject, most carefully pointed out the limits of 
inversion. He says: "It is indeed quite impossible to justify 
the process of inversion in any case without having some regard 
to the existential interpretation of the propositions concerned. 7 
Again, Welton says: "An inverse from a true proposition is 
not necessarily true when stated categorically. ... It is thus 
seen that these mediate inferences are of extremely small impor- 
tance ; we give them chiefly for the sake of completeness. 8 



b The word inverst is employed by mathematicians and logicians in 
several senses. Professor Royce defines the inverse as follows: "When- 
ever the proposition (a R b) is true, there is always also a relation, often 
symbolized by B, in which 6 stands to a. This may be called the inverse 
relation of the relation R. Thus if: "a is father of b," "b is child 
of a"; and if one hereby menus ''child of a father" the relation child of 
is, in bo far, the inverse of the relation father of." Ency. Philos. Sri., r, 97. 

1 Keynes, Studies and exercises in Formal Logic (ed. 4, London, Mac- 
millan. 1906), p. 217. 

- Manual of Logic, p. 305. 



IMMEDIATE INFERENCE 113 

But granted that inversion is a process that often yields a 
hypothetical conclusion — sometimes even doubly conditional — 
this does not destroy the practical value of these inferences. It 
is not true that a partial truth is no truth. The hypothetical 
conclusion is distinctly "better than nothing." All languages 
are full of ' * if s, and "if" they did not correspond to some- 
thing practical and also something theoretically defensible they 
would have been eliminated long ago. In the business of nar- 
rowing down the complexities of alternatives which we meet 
everywhere in the world of experience, we do not wait until we 
have achieved certainty. In our search for truth it is greatly 
worth while to be warned away from error by the destruction of 
hypotheses one at a time. This we saw is the function of the 
infinite judgment which some logicians have characterized as 
meaningless and worthless. 

There is a prevalent delusion among the enemies of tradition 
that Formal Logic is a collection of rules which furnish guid- 
ance of a positive character in the search for truth. But not 
even its most ardent defenders have held that it is a direct 
organon of knowledge. It is primarily by warning men away 
from error, that Formal Logic helps them in their efforts to reach 
truth. In deducing the inverse the logician does not, as has 
been asserted, 9 attempt the absurdity of proving foxes do not 
bark from all dogs bark. Now in the first place, before attempt- 
ing to draw any of the immediate inferences from All dogs bark, 
we must remember that this proposition is ambiguous, or to be 
more accurate, it is brimful of suggestions, meanings and impli- 
cations of meanings. It is in short a portmanteau proposition. 
The logician calls upon the grammarian to fix its meaning, for 
not until then can he determine with accuracy the implications 
or inferences from the meaning. We ask this proposition, among 
others, these questions, Do dogs exist; Is there anything that 
barks; Arc then brings other than dogs; Is there anything 



»Cf. L. E. Hicks, in an article on "Euler'a circles and adjacent 
space," Mind, n. s. XXI (1912), 413. 



Ill FOOTNOTES TO FORMAL LOCK' 

that dots not hark/ Also we may inquire (note now the double 
query), If then an beings other than dogs; are there any of 
Ik int/s that do not bark ; also, If there are beings that bark 
and if sown of these an not dogs, are there beings that art not 
dogs that do not bark, and how many. It is evident that some of 
these are questions concerning the meanings of the propositions 
and some are questions concerning the implications of the mean- 
ings. Some are first intensions and some second intensions. 
Among the former there is obviously the question of the existen- 
tial import of the proposition. The logician can not, indeed, 
peremptorily demand that these meanings be fixed, but he can 
Bay categorically that if they are not so fixed any doubt that 
remains will not affect the process of inference but only the 
conclusion. The inferential process, he insists, is unerring; it 
carries along unchanged any uncertainty that is handed to it. 
Now to the latter question, which it will be observed is the 
inverse, the logician replies, Yes, there are (on these conditions) 
sonu beings that are not dogs that do not bark. We see, then 
that the logician merely says he can warn you away from error 
in your quest for an animal that does not bark. You have 
been told that all dogs bark and you begin your search for an 
animal that does not bark, whereupon the logician tells you 
categorically that you must not look for the animal that does 
not bark among dogs, but if you are to find it at all it will be 
somewhere in the region of beings that are not dogs. The inver- 
sionist is prepared to treat a universal negative proposition in 
a like manner, although there is greater uncertainty about the 
neai lings of the original proposition. As I have remarked, he 
is not disturbed by the existential import of the proposition. It 
is a matter of common observation that the predicate in the E 
proposition need not exist in the same universe as the subject. 
lint this does not affect the process of inversion, or any other of 
the immediate inferences. Such restrictions as are imposed by 
the existential import of the proposition are passed on intact 



IMMEDIATE INFERENCE 115 

into the conclusion. We are challenged to find the inverse of 
No mathematician can square the circle and we are told that 
to do so we must perpetrate the absurdity of inferring from 
No mathematician can square the circle that Some one who is 
not a mathematician can square the circle. If this is all that the 
process accomplishes it would, indeed, he "inversion silliness." 
But here again, the real function of inversion is to warn you 
away from error. You set out in search of some one to square 
the circle. Having discovered that no mathematician can per- 
form the feat, you announce this to the inversionist, who there- 
upon replies, "if that is so and you still persist in your search, 
I can tell you most positively that if you are to find anybody 
who can square the circle, it must he someone among those iclw 
are not mathematicians." No inhabitants of Thessaly ever saw 
a centaur. The categorical inverse of this proposition, derived 
from a thrice-conditioned premise, would read. If no inhabitant 
of Thessaly ever saw a centaur and if anybody ever did, it 
must have been someone who was not an inhabitant of Thessaly, 
if there are any such. Dr. Mercier disposes of the inverse in 
his customary cavalier fashion. He says the inverse 

... is arrived at by a method so complicated that I will not trust myself 
to attempt it, but will take, from a standard textbook, the following 
example: "Every truthful man is trusted" — Inverse, "Some untruthful 
men are not trusted." Some logicians doubt the legitimacy of this form 
of Inference; and I must confess to misgivings about it; for, if it is 
valid, I see no reason why it is not equally valid to infer from ' ' Every 
truthful man is mortal" to "Some untruthful men are not mortal." This 
puts on inveracity a premium, which is scarcely to be expected from the 
justice of Providence; and, what is more to the purpose, does not seem 
to me to be implied in the postulate. 10 

But a valid non-contradictory inference of the hypothetical sort 
that I have described can be drawn by inversion from Dr. 
Mercier's example, Every truthful man is mortal, as follows: // 
every truthful man is mortal then if there are any beings that 
are not mortal they will be some of those beings that are not 



u>New Logic, p. 290. 



in; FOOTNOTES TO FORMAL LOGIC 

truthful men. And this is an inference thai a just Providence, 
to whom Dr. Mercier appeals, may safely accept. 

It is evident that the process of inversion is adequate to any 
o\' the several possible situations which the existential import 
of judgment imposes. Both subject and predicate and their 
negatives are existent in the same universe of discourse. This 
is assumed to be the ease where no information to the contrary 
is furnished the Logician when lie begins his task of inferring. 
If any other meaning is intended by the original proposition the 
Logician expects to be informed, for example (1) that neither 
subject nor predicate exists, (2) that one exists but not the 
other, (3) that either subject or predicate may be practically 
and perhaps theoretically without a contradictory. 

Now it should be remarked that we are not here concerned 
with the question whether this conclusion is a "new" truth; 
that is a question which concerns the whole class of so-called 
immediate inferences. Nor should we object seriously if some 
one should maintain that this process of inversion is neither an 
immediate nor a mediate inference as those operations are com- 
monly defined. There is a striking resemblance between inver- 
sion, when it is expanded into a form that exhibits all of its 
parts, and that one of Russell's "ten axioms" of Symbolic Logic 
which he has called the Principle of Importation. "The prin- 
ciple states that if p implies that q implies r, then r follows from 
the joint assertion of p and q. For example: "If I call on 
so-and-so, then if she is at home I shall be admitted" implies 
"If I call on so-and-so and she is at home, I shall be admitted." 11 

IV 
The criticisms of inversion which I have attempted to answer 
all resl bach upon an alleged failure to regard the existential 
import of propositions. Another objection has been raised, 



;i Principles of Mathematics, p. 10. 



IMMEDIATE INFEBENCE 117 

namely, that the process involves an illicit distribution. In "All 
8 is P," P is undistributed while in the inverse "Some non-S 
is not P," P has become distributed. I think there is here a 
serious misunderstanding as to the meaning of distribution. The 
medieval law concerning distribution stated that no term must be 
distributed in the converse if it was not distributed in the con- 
veriend. But now it should be observed that this law was 
intended only to apply to conversion, where the prior require- 
ment had been imposed, namely, that the quality of the proposi- 
tion must not be changed. However, in the obverse, retroverse, 
contraverse, inverse, the quality of the proposition has suffered 
a change in passing to the inference ; and here a different inter- 
pretation of distribution is required. The distribution of terms 
in negative propositions does not mean the same thing as the 
distribution in the affirmative proposition. The failure to 
recognize this fact, has brought confusion into discussions con- 
cerning the validity of inversion, as we shall see presently. A 
term is said to be distributed when we know something about 
every member of the class designated by the term. In the propo- 
sition "All S is P," S is distributed because we know something 
about every member of the class S, namely, that it is a P. 

But in the E proposition, "No S is P," while we may say 
again that S is distributed because we know something about 
every member of the class, this knowledge is of a different kind 
from what we had in the case of the A proposition. In "No S 
is P," I know something about every S, namely that it is not a P, 
and this I know indirectly. This indirect process, when made 
explicit is as follows : first and most fundamentally I know 
that "S is not non-S" and then because P happens to be some- 
where in the region of non-S (though I am quite ignorant of 
just where it is) I know that "S is not P." We met this diffi- 
culty in the chapter on the infinite judgment. We saw that 
negation is always a degree more remote from reality than 
affirmation. Every significant negation, when fully expanded 



L18 FOOTNOTES TO FORMAL LOGIC 

reads: Since P is in the region of non-8, and since 8 excludes 

//"//->' it excludes thai which is included in non-8, namely P. 

Hut now, referring to the diagram for the universal affirma- 
tive proposition on page it would seem that if P is undis- 
tributed, non-P should likewise be undistributed. This non-dis- 
tribution of P we have represented in the diagram by the dotted 
lines, indicating that the class P is undefined. So far as 8 is 
concerned, P might widen its sphere of application as far as it 
pleased, even to the extent of pushing non-P off the map of 
existence. However, if this dotted line marks the boundary 
between the two classes P and non-P, it would seem that non-P 
should have the same indefinite range as P. But we have not 
told the whole truth about the circle P when w r e have said that 
its expansion outward is unlimited, we must observe that its 
contraction inward is definitely limited. It is this lower limit 
which the very nature of the universal affirmative proposition 
permits us to disregard, that in turn becomes an upper limit for 
the expanding class non-P. Non-P may expand only to the 
limit to which P may contract. This anomalous fact is exhibited 
also in the process of ob version. In "All S is P," P is undis- 
tributed, but in its equivalent "No S is non-P," the non-P is 
distributed. 

But this apparent contradiction in the medieval law of dis- 
tribution when it was applied beyond conversion, did not attract 
the attention of logicians until the process of inversion was 
reached. Now although the difficulty has become more acute 
in the case of inversion, it is nevertheless in my opinion, precisely 
the same difficulty that has just been pointed out. Keynes 
noticed this difficulty in the apparent violation of the Law of 
Distribution and gave an explanation of it that has been followed 
by Oeighton and others. 

It will be remembered that we are at present working on the assump- 
tion that each class represented by a simple term exists in the universe 
of discourse, while at the same time it does not exhaust that universe; 



IMMEDIATE INFERENCE 119 

in other words, we assume that S, not-S, not-P, all represent existing 
classes. This assumption is perhaps specially important in the case of 
inversion, and it is connected with certain difficulties that may have 
already occurred to the reader. In passing from Ail S is P to its inverse 
Some not-S is not P there is an apparent illicit process, which it is not 
quite easy either to account for or explain away. For the term P, which 
is undistributed in the premiss, is distributed in the conclusion, and yet 
if the universal validity of obversion and conversion is granted, it is 
impossible to detect any flaw in the argument by which the conclusion 
is reached. It is in the assumption of the existence of the contradictory 
of the original predicate that an explanation of the apparent anomaly 
may be found. That assumption may be expressed in the form Some 
things are not P. The conclusion Some not-S is not P may accordingly be 
regarded as based on this premiss combined with the explicit premiss. 
All S is P, and it will be observed that, in the additional premise P 
is distributed. 12 

But now this is merely an elucidation of the difficulty not 
an explanation of it. The true explanation is to be found in the 
double meaning of distribution. Each term in a proposition, as 
we have just stated, has an upper and a lower limit to its exten- 
sion. Our attention need be directed towards only one of these 
limits, the other is ignored. For practical purposes we may say 
that we do have some genuine knowledge even if our class is 
bounded merely on one side. But for the purposes of exact 
thinking both the upper and lower limits must be observed, and 
this is what the doctrine of the quantification of the predicate 
attempted to accomplish. The inverse of the affirmative proposi- 
tion ''All S is P" is as Keynes has said, "Some non-S, is not P." 
It is indeed one and the same class P that is considered first with 
8 and then with non-S as subject. But in the one case we see 
P on its bounded or limited side and in the other the unlimited 
side. There is no contradiction, according to our point of view, 
in asserting that P is both distributed and undistributed. The 
quantification of the predicate is a device for looking at P 
from both sides at once. 



a Formal Logic, p. 139. 



120 FOOTNOTES TO FORMAL LOGIC 

V 

The theory of inference which I have proposed in these pages, 
namely, thai every true inference must mark a transition from 
a categorical to a modal proposition, removes some of the diffi- 
culties about the particular proposition. It is evident that, since 
the true particular is always a modal assertion the passage to 
such a particular is always a true inference. The particular 
judgmenl is always a problematic judgment in disguise. "Some 
8 is P" is equivalent to "S may be P." Venn, and other sym- 
bolic logicians after him, have denned some as not none. This 
is quite in agreement with one side of the popular meaning of 
the word. This definition provides an unambiguous relation of 
smiif to its lower limit none, but there is still an ambiguity in its 
relation to the upper limit, all. It may include or exclude all. 
This latter ambiguity, the popular mind also aims to avoid and 
so prefers the interpretation of some as not all, as well as not 

HOIK . 

Some is a variable moving toward a limit in two directions, 
but in different senses. In the downward direction tow r ard none 
it can not reach its limit, while in the upward direction toward 
all it may reach the limit. The particular proposition of ordi- 
nary logic on this view, is semi-indefinite, being defined by its 
exclusion of none and yet undefined by its inclusion of all. There 
are thus seen to be, theoretically at least, four possible relations 
between some and its limiting classes: (1) Some includes none 
and all, or (2) it excludes them both, or (3) it includes the all 
and excludes none, or (4) it includes none and excludes all. 
8onu lias been identified w r ith the indeterminate class of Symbolic 
Logic. This is, I think a mischievous error. The some of Tra- 
ditional Logics has never, even its most liberal interpretation 
included more than two of the four possible relations between the 
indeterminate class and its limiting classes, none and all. 

Every such discussion of the meaning of some that intends to 



IMMEDIATE INFEEENCE 121 

define it in terms of either its limits, all and none, presupposes 
that these limits themselves have already been defined. But now 
we should find it difficult to define none in any other way than 
by reference to some, and if none implies some, we move in a 
vicious circle in defining some as not none. We have here 
another illustration of what has so often been pointed out in the 
recent discussions, especially those inquiries into the nature of 
the fundamental concepts of mathematics, that when we deal 
with ultimate concepts it is impossible to avoid the circle in 
defining. 

It has been alleged that the particular proposition has for its 
collateral aim — if not its distinctive purpose — to assert that 
objects referred to by the subject do exist. When, for example, 
I say, "Some California Poppies are scarlet," my primary pur- 
pose is to assert the existence of such flowers and secondarily 
only am I concerned to give the information that their color is 
scarlet. It is evident that the primary function of the particular 
proposition is in reality what appears to be merely its secondary 
or indirect function. The particular affirmative proposition, 
''Some 8 is P," taken at its face value, means to affirm, but in 
practice its intentions is to deny the universal negative. Like- 
wise, the particular negative is employed to deny the universal 
affirmative. This latter fact is disclosed by the form which the 
particular negative so often takes in all languages, ' ' All S is not 
P," "Not All 8 is P." These forms, which perplex the student of 
elementary logic, are only rightly understood when the purpose 
to overthrow the universal is considered. 



CHAPTER VII 

THE CASE AGAINST THE SYLLOGISM 

I 

The syllogism has always been attacked on two scores. It is 
alleged, in the first place, that it is structurally defective — it 
begs the question. Secondly, it is held that it is not universally 
applicable. Mill criticized the syllogism on the former count 
and Bradley on the latter. In view of the various attacks, both 
ui)on the validity and the universality of the syllogism since Mill, 
and more particularly in view of the recent developments of 
Symbolic Logic the Aristotelian account of the subject demands 
a new interpretation. Aristotle defined syllogism as "discourse 
in which certain things being posited, something else than what 
is posited necessarily follows merely from them." This defini- 
tion contains five words each of which to say the least, is moder- 
ately ambiguous. Before the exact scope of this definition can 
be understood we must know (1) the nature of the "things 
posited"; (2) what we mean by "positing" or "laying down"; 

(3) in what the difference of the "something other" consists; 

(4) and what is meant by "following," especially (5) "neces- 
sarily following"? 

We may ask two questions concerning Aristotle 's own account 
of the syllogism. First, what precisely did he himself mean by 
the definition, as shown by the context. Secondly, granted that 
Aristotle's own discussion of the syllogism left certain forms of 
thought outstanding, is it possible to give a wider interpretation 
to the several words of his definition than he himself gave, so that 
the so-called asyllogistic types of reasoning may be encompassed 
by it '.' If we give to each of these five elements of the definition 

[ 122 I 



THE CASE AGAINST THE SYLLOGISM 123 

its most liberal interpretation, I believe it ean be shown that the 
case against the syllogism is not so damaging as the New Logic 
believes. 

The ordinary account of the syllogism as mediate inference 
is unsatisfactory because it is too vague. The difficulty of dis- 
tinguishing between the immediate and the mediate in thought, 
I have dwelt upon elsewhere. So, too. the description of the 
syllogistic process as a comparison of concepts lacks in explicit- 
ness. Again, Sidgwick, who differs from the other opponents of 
Formal Logic in his belief that the syllogism is the universal 
form of thought, proposes a definition which has a number of 
ill-defined terms. "A syllogism may thus be regarded as con- 
sisting of three parts: the rule (" major premiss") ; the identi- 
fication of a case as coming under it ("minor premiss") ; and 
the conclusion inferred as a result of applying the rule to the 
case." 1 If we interpret each of the words in the Aristotelian 
definition liberally, I think it can be shown that the syllogism is 
the universal form of thought. In its widest possible meaning 
it will be found always to consist in the correlation of genus, 
species, particular: or universal, particular, singular. I believe 
that every thought, be it true or false, will conform to this con- 
ception of syllogism. It is impossible to think otherwise than 
in this form. It is hardly necessary to say that this interpreta- 
tion of the syllogism is meaningless, or at least is plainly open 
to the two criticisms of lack of universality and begging the' 
question, if the relation between particular and species, and 
species and genus is taken in pure extension. These relations 
are sui generis; they are not to be confused with numerical or 
quantitative relations as ordinarily understood. The relation 
of particular to species is not the indifferent relation of the one 
to the many, nor is the relation of species to genus the merely 
associative relation of part to whole. The relation is vital and 
reciprocal. This relation might be expressed as universal, par- 



i Elementary Logic, p. 227. 



L24 FOOTNOTES TO FORMAL LOGIC 

ticular, individual; but we should avoid this designation, because 
the term individual is highly ambiguous in philosophy. In the 
nomenclature of Logic singular is preferable to individual. We 
should notice also thai ilu' term particular is ambiguous. For 
in the three fold designation, genius, species, particular, and 
universal, particular, singular, the word particular in the latter 
series corresponds to species in the former. But this ambiguity 
in the use of particular is in our common speech as well. We 
say, "(Jive me the particulars of this affair"; and again, "What 
particular sort of flower do you mean?" However, this am- 
biguity is not so important as in the case of individual. The 
latter is a difference in kind, the former simply a difference in 
degree. Individual usually means a single case. When I ask 
"What particular individual occupies that seat?" I mean to 
identify or to designate some particular one. But the word is 
likewise used in an entirely different sense, as when one says, 
"I like individuality." By this we mean the singular plus the 
evidences of self-activity. In this sense individual stands for 
spontaneity, life, growth. An individual is a fountain of ever- 
increasing newness and originality. This latter use of individual 
is not pertinent to Formal Logic, where a stick or stone is as 
good an individual as a soul. Thinking is always viewing in the 
light of genus, species, particular, or considering the relation of 
universal, particular, singular. "I think," means that I see 
this particular in the light of that species, and the species in the 
light of the genus, or else that I am carrying on the reverse 
process, seeing the whole or genus, and taking under it the 
species, and seeing the particular as under the species. Both 
the rigid syllogism of deduction and the un-rigid syllogism of 
induction are consistencies, and must be explained in terms of the 
threefold relation, genus, species, particular. 2 Syllogizing, or 



- This view of pan-syllogism I owe to the lectures of Professor Howi- 
Bon. An interpretation very like this has been given by Mr. Joseph, 
although he denies its universality. He says: "The central idea of 
Byllogism is that it works through concepts, or universals. The major 



THE CASE AGAIXST THE SYLLOGISM 125 

thinking together, therefore, always involves classification. "We 
can think inwardly from the whole, through the members, to 
the minutest members ; or outwardly from the minutest member, 
to the larger member, then to the class, and to the largest class. 
I am not unmindful of what I am committed to in the assertion 
that all thinking is syllogistic and that this always implies classi- 
fication. Symbolic Logic has shown that the definition of a class 
is the most important and difficult of all the problems of Logic. 
We may condemn the class view of predication, but we cannot 
escape from the fundamental fact of comparison that lies some- 
where at the heart of all judgment and all judgment about judg- 
ment. It may be, as Russell and McColl have asserted, that 
propositions are more fundamental than classes; this would not, 
however, affect the theory of pan-syllogism. Thought is a 
''relating activity"; from this there seems no escape. But an 
analysis of any act of comparison or the definition of relation 
reveals a number of difficulties. We cannot compare on the one 
hand total identities nor on the other hand complete disparates. 
Sameness without difference or difference without sameness makes 
comparison, judgment, or classification impossible. 

This syllogistic process is distinct from that of just perceiv- 
ing with the senses. The perceptive judgment is different from 
the cognitive judgment — the former is not a stage on the way to 
the latter. We do not classify when we see, or hear, or smell, 
that is to say we do not correlate, or see in a higher unity. In 
sense as such we do not have unity, only separateness. We may 
have a pseudo-unity in the association of sensations. Thought 
is the process of unification in which we harmonize so as not to 
obliterate the items. We retain their distinctness and discover 
the harmony between them. Or again, thought is a unifying 
process, by which we retain the clearness of each part in obtain- 
ing the wholp. Moreover, the two processes of unification and 



premiss asserts, not the presence of A in every f! (and therefore in C, 
among them), but the connection of A as such with B as such: hence 
wherever we fin<l B, we must find A." Introduction to Logic, p. 284. 



L26 FOOTNOTES TO FORMAL LOGIC 

separation vary inversely, paradoxical as it may seem. The more 
firmly the Integrating power clutches the items the more clearly 
docs the separating actively differentiate them. All this is appro- 
priately expressed in the name syllogism and without doing 
violence to its etymology or to Aristotle's own conception of its 
Bcope. 

I have already referred to the other aspects of this syllogistic 
fact which we need to notice before we can obtain a complete 
view. We still find the statement in textbooks that besides this 
one form, there are two others; that the syllogism is only one of 
flint forms of thought, namely: (1) conceptions or notions, (2) 
judgments, (3) the syllogism. The impression is still too often 
left with the student that we first have conceptions, and that we 
then pass on to the combination of these in judgment, and finally 
to the higher form in which three judgments are connected in a 
syllogism. Any such mechanical or corpuscular theory of thought 
is faulty. Thought is not a mere aggregation of symbols of 
thought. The nature of thought is to produce its own elements; 
it creates both itself, and its members. Thought is a whole, so 
whole that it furnishes to itself its own members and also com- 
bines them. The reciprocal process of determining the whole 
into its elements and the elements into the whole, constitutes the 
fundamental distinction of deduction and induction — the rigid 
and the un-rigid syllogism. 

But hereupon it may justly be asked where do we get the 
distinction between the relation, conception, judgment and 
reason, and the relation genus, species and individual? To this 
query we can only reply that both relations are fundamental, 
lmanalyzable and indefinable. We just think our thoughts, and 
cannot but think them. Every conscious experience that we call 
thought must stand the light of a syllogism, else it is not a real 
experience. If we cannot think, that is, syllogize our experience, 
we do not have any. As to the series, concept, judgment, 
syllogism, we cannot get along without these names, but the 



TEE CASE AGAINST TEE SYLLOGISM 127 

syllogism is riot the last result or product from the union of 
judgments, that were themselves the products of concepts. The 
concept is not the ultimate element of thought ; on the contrary 
the thought unit is the syllogism itself. 

The syllogism is the omnipresent, all-embracing form, denned 
as the thought that casts itself in the correlated distinction of 
particular, species, genus, or universal, particular, singular. 
These three distinctions each depend for their meaning on the 
correlation of the three. A significant, "just this" always pro- 
vokes the query ' ' just this what ? ' ' Hence it is necessary to tell 
the species. Someone says to me, ' ' I want you to see this " ; I 
immediately ask, "this what?" Now if I really do see it, it is 
this or that or the other object that I see. It has correlation 
(shape, size, color, etc.), and through this correlation it is con- 
nected with the species. In looking for the this, we see the color 
or the shape, and so we connect it directly with species. If we 
did not take in the others of the species we would not see the 
this. The singular means nothing except in the light of the 
particular, and the particular means nothing except in the light 
of the universal. All perception, all intelligence, is knowing in 
the light of the whole. Conversely, the whole means nothing 
without the final this. Without the descending steps in the cor- 
related things, it is not a whole, it is nothing. The universal 
without the species and the genus, is an abstraction, is nothing. 
The abstract singular and the abstract universal are alike noth- 
ing. Hence a thing that does not contain its own differentia does 
not exist. 

The syllogism cannot proceed without having parts and a 
whole upon which to operate. Parts that are just parts — that 
have no relation to any whole, have no meaning. They are parts 
of nothing and so are themselves nothings about which nothing 
can be asserted. Furthermore no judgment is ever just the sum 
of units that existed prior to the whole which they constitute. 
The quantitative whole which seems to be composed of units 



L2fi FOOTNOTES TO FORMAL LOCK' 

qualitatively alike is no exception. This is reached by a process 
o\' abstraction in which the parts, having become qualitatively 
indifferent to each other, have also sacrificed their unique rela- 
tions to the whole. The whole is thus lost to sight when it is no 
Longer required as the synthesis of the different and differing 
tads. But no whole, not even the abstract quantitative whole, 
may disappear entirely. Quantity is just the latent device for 
holding asunder parts which are qualitatively alike. This thought 
I shall develop further presently. 

The singular is not made up out of the universal, nor the uni- 
versal out of the singular, nor the particular out of either. 
Neither can we start with the all (which is an empty name when 
taken alone) and from it arrive at the particular, and so pass 
on to the singular. For this is equivalent to starting with noth- 
ing, and trying to make of it a lower class, and of this in turn 
still a lower class, the final result will still be nothing. We cannot 
think these things apart ; without the particular and the singular, 
the whole is nothing, they are all intrinsically correlated, and are 
not to be taken apart. The syllogism is not a composite, nor an 
analysis of a composite, but an individual whole furnishing 
intrinsically its own elements. Thus- it is clear that no one of 
the three forms of thought sets out with one unanalyzable ele- 
ment. We do not begin, as the empirical theory of association 
would have us begin, with thought atoms, then proceed with 
combinations of these. The syllogism is a harmonic unity, a 
unity of correlated elements existing intrinsically in correlation. 
The syllogism in this sense, we repeat with insistent emphasis, 
is the cardinal fact wherever there is a thought ; it is the universal 
type of thought. 

II 

It is however, insufficient to say that the syllogism is the uni- 
versal form of thought, differentiating itself into the syllogism 
as concept, the syllogism as judgment, and the syllogism as argu- 



THE CASE AGAINST THE SYLLOGISM 129 

merit, or that it is the universal, omnipresent form of thought, 
the indivisible, correlated unity embracing universal, particular 
and singular. We must show how and why this correlation 
appears in three different ways. There is need in short of dis- 
tinguishing between the implicit and the explicit presence of the 
syllogism. In the concept, the syllogism is only implicitly pre- 
sent. To bring the implication out in the clearest way, it is 
necessary to show, as we have in part already shown, that judg- 
ment is implied in the concept. It is so implied, since the con- 
cept means nothing unless it is a whole, ensphering a great many 
marl's, or implicit judgments. And it has therefore rightly been 
said that in judgment, we explicate the corresponding concept, 
which is the subject of the judgment. In the judgment we say 
that the concept is so and so. If I assert that I have a concep- 
tion, and I am asked what my conception is, I answer by making 
a series of judgments. For example, I am asked, "What is a 
salamander?'' I reply, "It is a reptile, it is scaly, it can stay 
in the fire without being burnt, etc." Here I am explicating the 
concept, salamander, by making a number of judgments bring- 
ing out the various characteristics of the salamander, in each of 
which judgments I employ a predicate and connect it with the 
concept by a copula. The concept (as a thought) is therefore an 
implicit bundle of judgments. So, also it may be shown that 
every judgment is an implicit syllogism. Suppose that I assert 
"XisY." You ask, "What is it to be Y?" I answer "Y is Z." 
Then of course "X is Z." The filling out of the required mean- 
ing of the judgment makes us go on and complete the syllogism. 
We can continue in this way indefinitely, until we come to a 
predicate beyond which we cannot go. This implied process in 
thought is seeking the real whole, from which each part takes its 
significance. 

Every thought implies two elements and their union in a 
third. All reasoning is from particular to particular via the 
universal. This uniting act Formal Logic has always preferred 



L30 FOOTNOTES TO FORMAL LOGIC 

to call the copula. The word is appropriate, yet in one sense 
quite inappropriate, for copula really means a link or yoke, and 
suggests an artificial union ; we are apt to think of it as uniting 
two distinct things. But the elements united in thought are not 
two distinct things. The truth is, the syllogism is an indivisible, 
complex, unitary act, and the copula furnishes the principle 
which both joins and separates the parts of the whole. It is the 
function of the copula to "couple apart." Bosanquet writes: 
"In analysing the judgment as an act of thought we may begin 
by dismissing the separate coupla." 3 To this we may yield a 
luarty assent, but there is no good reason why the word itself 
should not be retained to designate the real act involved in the 
synthesis of subject and predicate. The copula is the inner activ- 
ity that permeates each of the tw r o parts and grips them into 
a whole. Two pieces of magnetized iron that cohere are a better 
illustration of the function of the copula than the link between 
two cars. In the case of the two pieces of iron, every molecule 
in each piece takes part in the enwholing grip. In terms of this 
act of joining through the copula, we can determine the distinc- 
tion between the concept, the judgment, and the syllogism. The 
difference between these three is a difference in the degree of 
explication of the copula. In the concept, the copula is not 
explicit at all, but implicit. In the judgment, the copula is 
explicit, but appears simple, as though on the surface, having no 
complexity. In the syllogism, the complexity of the copula comes 
entirely into light. 

It is not only convenient, but necessary for the purposes of 
exposition and communication of thought, to adhere to the dis- 
tinction between dynamic and static relations and to say that 
the syllogism is competent to deal only with the latter. This is, 
however, a distinct ion that has to do with "thought expressed"; 
it does not concern "thought in reality." Such a distinction 
blinks at the real difficulty. The dynamic relations themselves 



'in is of Logic, p. 99. 



THE CASE AGAINST THE SYLLOGISM 131 

cannot exist, or at least cannot be thought, without a universal 
within which the apparently intransitive relations are enclosed. 
Now there are in reality no purely intransitive relations. Even 
in the temporal series the present harks back to the past — the 
effect in a sense causes the cause. Yet the dynamic order and 
the static order have something in common, and it is the task 
of Logic to discover this pervading element. It is, of course 
true that any reasoning which explains phenomena through 
causes is not syllogistic in the narrower interpretation. But 
when we take the larger view of syllogism as thought exhibiting 
itself in the threefold relation of singular, particular and uni- 
versal; or particular, species and genus, we find that reasoning 
through 'causal determination is no exception to its scope. 

Common sense reads class relationships in one direction only. 
It supposes that in any series of more and more inclusive groups 
the stability of the smaller group must give way if it interferes 
with the stability of the larger. The part is subordinate to the 
whole. This seems an elemental truth. But the discernment of 
this truth as an axiomatic principle is a far simpler matter than 
its practical application. In what does the stability of any group 
consist, and what constitutes interference with the stability of a 
larger group, and what precisely constitutes a larger and a 
smaller group ? Merely a cursory examination of group rela- 
tions reveals the hidden truth that some aspects may always be 
found in which the smaller includes the larger. In extension the 
species is included in the genus, but in intension the genus is 
included in the species. The principle of total one-way inclusion 
seems a chimera. There appear to be no groups such that the one 
is in every way included within the other. Real groups involve 
only transitive and symmetrical relations. The relation between 
a so-called small group and its including larger group must ever 
exhibit the fundamental relation between part and whole, in 
which, as we have seen, the parts and the whole are equally real ; 
each includes and is included by the other. Neither presupposes 



FOOTNOTES TO FORMAL LOCK' 

the oilier, nor is either more real than the other. Neither has a 
stability to which the other owes, in every way, unquestioned 
allegiance. Such a view of class relations will, I believe, go far 
toward vindicating the universality of the syllogism. 

The most difficult and, I believe, the most important of all the 
problems of Logic is the relation of extension to intension. Upon 
this distinction depend the vital questions of the meaning of 
class, the import of judgment, the fundamental metaphysical 
question of the relation of quantity to quality, and above all the 
question of the validity and universality of the syllogism. The 
elementary textbooks find little difficulty with this subject for 
there is a superficial definition of these words that makes this 
relation simple and comprehensible enough. Some writers have 
been aware of the difficulty of defining each of these words in a 
way that would make their relation in one object intelligible. 
Jevons, for example, says "I believe that the reader who once 
acquires a thorough apprehension of the difference of these mean- 
ings, and learns to bear it always in mind, will experience but 
little further difficulty in the study of Logic." 4 However, 
Jevons' own treatment of the subject is most naive and ignores 
entirely the real issue, namely, the essential incommensurability 
of the extensive and the intensive series. Aristotle taught that 
the extensive and the intensive modes of predication were, at 
bottom, equivalent and the question of priority meaningless. He 
declares most explicitly that there is no difference between saying 
that one thing is entirely included in another and saying that 
the other thing is always a predicate of the one. 5 Mathematics, 
until very recent times, has always glorified quantity, and the 
older symbolic logicians taught that the point of view of extension 
was so fundamental in all our thinking that intension might be 
entirely disregarded. The philosophers, on the other hand, 
insisted on the primacy of quality, and declared that the relation 






i Elementary Lessons in Logic (New York, Macmillan, 1914), p. 37. 
■ < !.f. Prior Analytics, I. 



THE CASE AGAINST THE SYLLOGISM 133 

between subject and predicate was distorted from truth in the 
extensive interpretation of judgment. Mill and many writers 
since have insisted that the intension of terms must be taken as 
both psychologically and logically primary, and extension as 
secondary. Mill, to be sure, held that some terms have no conno- 
tation, but only denotation, and that such terms always denoted 
the subject directly and connoted its attributes indirectly. But 
this was the interpretation of the relation for the purpose of 
communication. Mill himself plainly implied that in thought 
connotation is primary; but since we rarely have the qualities 
in a sufficiently definite and tangible grasp, we resort to the 
denotation in defining or describing the object. A familiar illus- 
tration of this is found in ordinary intercourse where we often 
find it more convenient to describe an object by telling where 
it is than what it is. But in all these debates concerning the 
meaning of extension and intension and the nature of their 
relation, the contestants never suspected that there might be 
intermediate positions between extension and intension ; or, that 
since a good case could be made out for the priority of each, 
perhaps neither was fundamental but that both were correlated 
aspects of a more fundamental point of view. 

The first difficulty that the naive treatment of the relation 
of connotation to denotation met was the obvious fact that the 
law of inverse variation was not universally applicable. It is not 
strictly accurate to say that as the extension increases the inten- 
sion decreases and vice versa. In the calculus of classes where the 
distinction between subject and predicate is effaced and the con- 
tent of proposition represented diagrammatically as by Euler 
and Venn, this may be partly true. However, it is not a faithful 
account of the psychological process involved. The power of 
thought to widen its field of attention is not incompatible with a 
simultaneous deepening of its intensive insight. It is a common 
practical occurrence and one that has a deep-seated theoretical 
justification, that, in extending its synthetic grasp over new 



l.;» FOOTNOTES TO FORMAL LOGIC 

instances, thought is continually discovering attributes hitherto 
Latent. In considering the subject of analysis and synthesis in 

judgment, and the con-elated question of novelty and sameness, 
I attempted to point out how essential it was to any right under- 
standing of the import of judgment to see that the synthetic 
and the analytic functions of thought may both operate each in 
its own opposite direction. No antinomy is involved in describ- 
ing certain systems as exhibiting simultaneously integration and 
differentiation. 

The relation of extension to intension, of quantity to quality 
is of such vital importance that I wish to pursue this matter still 
farther even at the risk of indulging in subtleties that may appear 
to the reader quite out of place in the present discussion of the 
nature and validity of the syllogism. No idea, which is in the 
least extended — that is, no quantitative idea can be brought into 
consciousness by one indivisible act. Any single pulsation of 
consciousness does yield size, that is Gestalt-Qualitat or form, 
just as it does quality ; but such a simple act of consciousness can- 
not give ua the notion of extension regarded as a system of inter- 
related parts. The notion of true quantity never comes to us 
in a single beat of consciousness. It is a continuous manifold, 
and yet a manifold which, though never grasped by one indivi- 
sible act of mind, is on the other hand equally incapable of being 
produced by a mere repetition of units, or ultimate, simple ele- 
ments. We have here, again, the perennial problem of the rela- 
tion of the part to the whole, of individual to species, of a term 
to the class of which it is a member. This problem is so closely 
connected with the question of the relation of quantity to quality, 
that we may partially solve the difficulty, I think, if we examine 
it where it appears in another form, namely, in the relation of 
the arithmetical to the geometrical continuum. 

Modern mathematics has discovered that the arithmetical 
and the geometrical continuum are different facts, both for 
description and explanation. We never pass directly from one 



THE CASE AGAINST TEE SYLLOGISM 135 

to the other either in practice or in theory. The geometrical 
continuum resists any attempt numerically to exhaust its mean- 
ing; and the arithmetical continuum can never be regarded as 
the first step in the logical process of the development of the 
geometrical continuum. All such attempts to derrve one con- 
tinuum from the other are vicious circles. When we respond to 
the demand for an absolutely single and simple element, we find 
that the spatial continuum, which is quantity or extension par 
excellence, presents insuperable difficulties to conceptual analysis. 
The mathematician responds to this challenge to find ultimate 
elements by declaring. ' ' There are points. ' ' But, when required 
to define these points, he finds that they are just the self-con- 
tradictory outcome of this search for the ultimate elements. This 
definition is self-contradictory for the reason that when the 
mathematician reverses the process, he discovers that he cannot 
get back from his points to the continuum from which he started. 
No repetition of the point, as such, can give rise to the line, that 
is, not the continuous or quantitative aspect of the line. We have 
here the familiar paradox concerning the discrete and the con- 
tinuous aspects of quantity. Because of its incapacity to pene- 
trate things to the bottom of their real natures an imperfect 
mind must resort to a quantification of them. Let me illustrate : 
and 0' are two objects which are qualitatively alike differing 
only in quantity, that is, they are members of a lowest species. 
Thought first contemplates the object by itself. It discovers 
that it is unable to penetrate the object to the core of its mean- 
ing. A certain opacity prevents the finite mind from ever reach- 
ing the essential, individual nature of 0. But is not yet a 
quantity, for quantity is never the content of such a single pul- 
sation of consciousness. Baffled in its attempt to discover the 
true nature of by internal searching, thought seeks for that 
desired information from an external source. It betakes itself 
to the other of 0, or 0' , which is, however, in itself just as 
impenetrable for thought as was. and 0' are conceptually 



L36 FOOTNOTES TO FORMAL LOGIC 

alike, and yet the mind perceives a difference between them. 
Every attempt to explain this difference lands us in an inevitable 

contradiction. 

But now in this second pulsation of consciousness the quanti- 
tative aspect of and 0' has suddenly appeared. Quantity is 
that mysterious somewhat that can not be found in either or 0' 
when contemplated alone but does somehow seem to exist in 
each when both are viewed together. Quantification might then 
be described as the result of our finite efforts to discover exter- 
na lly the inaccessible internal meanings of things. Or I might 
say it is the search for a mediator between objects where the com- 
plete understanding of each is by the very nature of things 
impossible. 

Herein lies also the solution of the apparent contradictions 
in the discreteness and the continuity of quantity. The dis- 
creteness arises from the necessary duality of the thought pro- 
cess that produces the quantitative way of viewing things. The 
continuity is simply the compulsion under which thought lies of 
holding the two objects and 0' in a unitary grasp of conscious- 
ness in order to explain the unfathomable mystery of each. From 
the absolute point of view and 0' of our illustration, instead 
of being covered by one concept, are provided each with a con- 
cept of its own which is adequate to its essential nature. A 
perfect mind has no need to view things under the category of 
quantity. For finite thought quantity is simply the ever present 
reminder of the irrationality of sense. Finite thought is, once 
for all, inadequate to sense. Every this that it contemplates is a 
this only in appearance. To our limited minds the this reveals 
only its thisness. But, as I have already pointed out, the thisness 
of the this contains as a part of its meaning a reference to a that. 
And now comes the crucial point. Finite thought feels itself 
irresistibly impelled to search for the that to which the this 
points, which in reality it must mean to be a this. The mind 
at once discovers that it has entered upon a hopeless, an unending 



TEE CASE AGAIXST TEE SYLLOGISM 137 

task; for, no sooner do we discover the that, which we had hoped 
would solve the inexplicable mystery that enshrouds the this, 
than it turns out to be not a that at all, but the identical this 
from which our thought started. Thought has in a fashion, to be 
sure, solved the puzzle; but in the solution it has likewise rein- 
stated its original question. Here we find an explanation not 
only for the discreteness of extension and its continuity, but also 
for its infinitude. The process described is evidently of the 
recurrent type, but I think it differs in one essential feature from 
the Kette that Professor Koyce has so often described. In the 
present Kette, the process is in the end a tautological one. Each 
new member of the Kette has novelty only so long as it is con- 
templated as a fact still external to the series, that is, as the goal 
toward which each individual pulsation of thought strives for 
the moment. But as soon as the goal is reached — when once that 
new link has been welded into connection with the rest — the 
novelty it formerly possessed vanishes into an inevitable same- 
ness with the whole. The novelty is only a transitory aspect of 
the essential tautology in the process. The novelty is accountable 
for the discreteness of extension, the tautology for its continuity. 

Ill 

If the syllogism is merely an expression of the relation of 
classes, where each class is taken in extension only, that is, where 
the thought is uni-directional, it will truly not compass all the 
forms in which we may reason. Such class reasoning always con- 
forms to the following type: (1) the major premise is an enum- 
erative, universal proposition in which we affirm that each 31 
is seen (by actual observation) to be in the class P ; and (2) the 
minor premise states that S is observed to be one of these M's; 
then (3) the conclusion, £ will be in class P. This view of the 
syllogism has rightly been condemned, firstly, because of its 
evident tautology and secondly, because it is not universally 
applicable. The first of these criticisms, namely, that it is a 



L38 FOOTNOTES TO FORMAL LOGIC 

petitio appeared Long before Mill's classic assault. Ii was 
advanced frequently by Aristotle's own students. The second of 
the criticisms is very prevalent in recent discussions. As has 
now so oil en been pointed out by Bradley, and others, there are 
many tonus of inference, for example, those that are concerned 
with dynamic relations, in which there are no class relationships, 
or in which we are not conscious of any such relations. I think, 
however, that all such relations can be compassed by the class 
relations when they are given the interpretation I have offered. 
It is an unwarranted limitation of the scope of the syllogism 
to restrict its application to the old class view of judgment. 
There is no mention of classes, that is, classes in extension, in 
Aristotle's definition of the syllogism: "Syllogism is discourse 
in which from certain things laid down other, different things 
follow." The things "laid down" in the major premise are not 
"laid down" according to any principle of inclusion or exclu- 
sion. Aristotle was obliged to distinguish (as every logician 
must) between thought and language. In the actual thought 
process the relation of an individual to a class was for Aristotle 
always a relation in intension. But when this intensive relation 
was translated by him into a form available for exposition and 
communication it took the inevitable form of a relation in exten- 
sion. The charge of a petitio can not be brought against the 
present pan-syllogism. It employs the true universal which is 
an assertion about things before they have been experienced, 
and which is in a sense, therefore, always hypothetical. Now 
since the major premise is hypothetical, and the conclusion is 
categorical, it is impossible that the latter could have been con- 
tained in the former. Moreover, when it is said that the conclu- 
sion contains "new" knowledge, it is not knowledge that is 
totally disconnected from the premises; for no process of infer- 
ence, mediate or immediate can ever deliver such new knowledge. 
It is n<\v knowledge in the sense that it is then for the first time 
6bBi rved. 



THE CASE AGAINST THE SYLLOGISM 139 

There is abundant evidence everywhere in Aristotle's treat- 
ment of the subject that he was fully aware of the two kinds of 
universal propositions — the abstract or pseudo-universal which 
is a collection of actually observed particulars, and the true or 
concrete universal, which (by asserting a connection of attri- 
butes) refers not to any definite group of individuals, but to an 
entirely indefinite group. The pseudo-universal, "All S is P," 
means, "Each S (and I have examined and counted them) is a 
P." The true universal "All S is P," means "S as such is P, or 
if S then P. The question whether the syllogism in its applica- 
tion of the dictum de omni et nullo involves a petitio as I have 
said hinges on the sense in which we take the major premise. If 
this is construed as an historical or enumerative judgment, then 
manifestly the conclusion is just one of the particulars which 
has gone into the aggregate, bound together by the all in the 
major premise. The so-called universal, that is, the enumerative 
or historical universal is itself merely an aggregate of particular 
truths and has no greater validity than the particulars which 
constitute it — it is itself another particular. Aristotle pointed 
out, and it was an insight that always seemed irrefutably clear 
to him, that the universal nature of an object could never be 
reached by examining and counting particular instances. 

But even in a syllogism, where the major premise is a pseudo- 
universal, just an aggregate of observed individuals, there is 
often a movement in thought, in which there is novelty in the 
conclusion. The major premise although strictly an enumerative 
universal, does not contain the conclusion nor even predict it. 
The two premises have come to us by different routes and it is 
only in the combination of the two that the conclusion is reached. 
For example, if a man should learn from the telegraphic reports 
that the entire Second Regiment were taken prisoners in the 
battle of the Marne, and then on consulting the lists in the "War 
Office should find that his son was enlisted in this Second Regi- 
ment, the conclusion that his son was captured is something over 
and above the agony of suspense that came from the unsupported 



lie FOOTNOTES TO FORMAL LOGIC 

major premise. To the authorities in the War Office, who have 
before them at one time, both the telegraphic report and the 
record of enlistments, there is not the novelty in the conclusion 
that there is for the anxious parent. 

In the per feet mind premises and conclusions are concomit- 
ants not s((jut n(s. and hence all reasoning in such a mind would 
involve an essential tautology. But for the purpose of com- 
municating its intuitive knowledge to minds on lower levels of 
insight the perfect mind would employ the syllogism and the 
accusation of tautology would be unjustified. On this view, then, 
the syllogism is the instrument of communication between 
minds having different degrees of insight into the relations among 
things. The perfect mind would not syllogize, nor would imper- 
fect minds, if they all had simultaneously the same degree of 
knowledge of facts. 

Bradley has condemned the syllogism at times with vitriolic 
vocabulary. The mildest of the epithets that he has applied to 
it is "a chimera." And yet he often comes quite near to con- 
ceding all that its defenders have thought worth contending for. 
He says: "If it were admitted, on one side, that the syllogism 
supplies no general type of the reasoning act, it might be allowed, 
on the other side, that it is a mode of stating the principle which 
is used in that act. It is universal as a form for showing the 
explicit and conscious exercise of a function. 5 This is an admis- 
sion both of a form and of its universality. The formalists have 
never claimed for any of the forms of thought an existence prior 
to and separated from its concrete setting. They have granted 
freely that there are no antecedent types or schemes for thought. 
The form of thought as we have shown in an earlier chapter 
is a vital constructive principle within the so-called object matter 
of thoughl itself. There is some thing in every concrete act of 
thought that always detaches itself from the thought, something, 
as Bradley himself has said, that is "more abstract than the 
argument itself."* 

a Principles of Logic, |>. 482. 



THE CASE AGAINST THE SYLLOGISM 141 

IV 

It may not be evident to the reader how much the foregoing 
discussion owes to Kant's well-known defense of the syllogism. 
The logical doctrine of marks taught by Kant has had contempt 
heaped upon it, particularly by Hegel, who holds it responsible 
for much of the confusion in the discussion of the nature of im- 
mediate and mediate inference. Hegel said : ' ' There is no more 
striking mark of the formalism and decay of logic than the 
favorite category of the 'mark.' : Kant's account of the doc- 
trine has, I venture to think, been much misunderstood and 
maligned. It will be remembered that he denned judgment as 
the comparison of a thing with some mark, and ratiocination as 
a judgment by means of a mediate attribute. And, the supreme 
rule of all ratiocination he stated thus: "A mark of a mark is 
a mark of a thing itself." Nota noiae est nota rei ipsius. 

The criticism that Kant did not prove his dictum deserves 
only passing attention. It would not be the highest or final 
rule if it were capable of proof. Any attempt to prove the 
supreme formula of all ratiocination would be to reason in a 
circle. Proof would be possible only by means of one or more 
inferences. This principle claims to be the final anchorage of 
all certainty in reasoning and can no more be challenged than 
the indemonstrable propositions of Symbolic Logic. The two 
criticisms which Joseph 7 has urged against Kant's principle are 
more pertinent. However, neither of his objections appears to 
me a serious indictment. The first is that the rule assumes the 
minor term is always a concrete thing. Kant would have 
admitted, I think, that this was precisely his intention and would 
not have differed widely from Bradley's view that the subject in 
every judgment is reality or some definite and therefore con- 
crete portion of reality. The ipsa res of Kant's formula is just 
this presented reality to which the ideal content is referred. 



Introduction to Logic, e<l. 2, p. 307. 



L42 FOOTNOTES TO FORMAL LOGIC 

However much we may differ from Bradley's theory of judg- 
ment, it Beems to me thai his central contention thai the subject 

is a concrete datum is unescapable. I do not see therefore that 
Kant s supreme rule differs essentially from Bradley's definition 
of inference as the indirect reference of a content to reality. 
The ideal content, meaning, or attribute is attached to reality, 
no1 directly but indirectly by being joined to a meaning already 
attached. 

The second objection to the formula is that it makes one attri- 
bute qualify another. This, too, seems an immaterial criticism. 
In the first place we may contend that there is nothing contra- 
dictory in the statement that there may be an attribute of an 
attribute, as Joseph seems to imply. Wherever an object admits 
rank or psychological priority among its attributes, a later attri- 
bute, being an attribute of an object already qualified, is in 
reality an attribute of an attribute. Also the varying degrees 
in intensity of the quale of sensations are in a sense qualities 
of qualities. But admitting that there may be an inherent diffi- 
culty with the conception of an attribute of an attribute (con- 
struing the expression literally) I think this is not precisely the 
meaning that Kant intended by the expression nota notae. Mark 
of a mark, is the better rendering of nota notae than attribute 
of an attribute. 9 The working of Kant's formula may be illus- 
trated in the syllogism, Savages are cunning, Indians are savages, 
therefore Indians are cunning. Cunning is the mark of savagery, 
and savagery is the mark of the Indian, therefore cunning is 
the mark of the Indian. Of the three terms in the syllogism two 
are always taken in connotation, namely, the major and the 
middle. The minor must always be taken in denotation. In the 
major premise, both subject and predicate are taken in connota- 



s It must be observed that the word mark has two meanings. It points 
both forward and backward; it is the sign or evidence of something that 
has been, as well as the prophecy of something yet to come. The. glacial 
BCOrings are the marks of the ice-age, while a red sunset is the mark of an 
impending storm. 



TEE CASE AGAINST THE SYLLOGISM 143 

tion ; it affirms that the attribute of cunning accompanies the 
attribute of savagery. But in the minor premise only the predi- 
cate is taken in connotation. 

Kant maintained that the dictum de omni was subordinate 
to his formula, "Whatever is a mark of a mark of a thing is a 
mark of the thing itself. ' ' The former declares that whatever is 
true of the concept is true of everything contained under it. 
This, according to Kant represents a stage in the process of 
abstraction one step removed from the formula. The concept 
itself was derived in the first instance by abstraction from the 
things which came under it. Thus whatever belongs to this 
concept will in truth be an attribute of an attribute and therefore 
an attribute of the things from which it has been abstracted. 

Kant drew a distinction between pure and hybrid mediate 
inferences, that we have lost sight of in our later discussions 
about the universality of the syllogism. The pure inferences 
are those which require but three propositions. We have a hybrid 
inference when between two of the main propositions there 
must be interposed a fourth proposition which is itself an imme- 
diate inference from one of the others. Kant made this distinc- 
tion the starting point of his essaj^ on ' ' The Mistaken Subtlety of 
the Four Figures." He regarded the first figure only as pure 
rationcination, since it involved never more than three propo- 
sitions. 

It is not my purpose to enter into a long discussion of the 
relation of the later figures to the first. Without detailed proof 
I shall say that I believe Kant's position to be fundamentally 
correct. I am sure, also, that Kant would have explained all of 
the modern asyllogistic types of reasoning as ' ' hybrid inferences. ' ' 
In his exposition of the fundamentals of Symbolic Logic, Russell 
has postulated ten indemonstrable axioms, the sixth of which is 
the syllogism as it is commonly understood. But on our wider 
interpretation of the syllogism, I believe, all of the other axioms 
can be explained as either abbreviated or expanded forms of 



Ill FOOTNOTES TO FORMAL LOGIC 

the fundamental syllogistic fact — thought exhibiting itself in 
tin 1 triadic relationship of universal particular and singular. 

Lei tne explain by quoting Russell's seventh axiom: "If q 
implies q and r implies r, and if p implies that q implies r, then 
pq implies /*. This is the principle of importation. In the hypo- 
thesifl we have a product of three propositions; but this can of 
course be defined by means of the product of two. The principle 
slates that it' p implies that q implies r, then r follows from the 
joint assertion of p and q. For example: 'If I call on so-and-so, 
then if she is at home, I shall be admitted/ "° I fail to see why 
this can not be explained as a triadic relation. In fact, Russell 
seen is to resort to such an explanation himself when he says 
that the hypothesis, although it has three propositions, can be 
defined by two. Every thought contains three and only three 
terms, that is, there are only three fundamental nodes or beats. 
This needs further elucidation. All reasoning is (as we have 
often had occasion to remark) a movement from particular to 
particular via the universal. It follows that every inference 
must have three terms, and that no inference can have less nor 
more. Inferences have often to do with more than three facts. 
But it is important to distinguish between terms of inference, 
that is the significant nodes in the movement of thought and the 
data of inference, that is, any accidental halting-places. Each 
of the three terms may be viewed as a system and when its 
secondary data are combined with the secondary data of each of 
the others, we get hybrid inferences with apparently more than 
three terms. To use a railway figure of speech, the main trunk 
line of thought has three stations where the "train of thought" 
must stop. There may, be any number of intermediate stations, 
however, where it may stop. 

There have been many attempts to give a syllogistic demon- 
stration of the so-called axiomatic truths and many refutations 
of these attempts. Bradley has said, "To prove syllogistically 



9 Principles of Mathematics, p. Itf. 



THE CASE AGAIXST THE SYLLOGISM 145 

that, because A and C are both equal to B, they are equal to one 
another, is quite impossible.' 7 Also, "I may suggest to the 
mathematical logician that, so long as he fails to treat (for 
example) such simple arguments as "A before B, and B with C, 
therefore A before C," he has no strict right to demand a hear- 
ing." 10 Euclid's first axiom, "Things equal to the same thing 
are equal to each other," has been written in syllogistic form 
thus : 

Things equal to the same thing are equal to each other. 
A and C are things equal to the same thing. 
And .-.AC are equal to each other. 

But in this syllogism both the major and the minor premises 
are defective. The major premise in the syllogism is the axiom 
itself, and hence not a major premise in the required sense of the 
word. It would be circular reasoning, vicious in the first degree 
to use the identical proposition, which is to be proved. The 
major premise ought properly to read, Things equal to B are 
equal to each other. But a more serious fault we find in the 
minor term, A and C. In the concrete instance of the axiom 
A = B, B = C . •. A = C. A and C function separately each as 
a distinct subject. But in the minor premise of the syllogism, 
by means of which we attempt to validate the axiom, we take 
unwarranted liberties with A and C by attempting to make 
them function conjointly as a single subject. A and B are, is not 
the same as A is and B is. It is not the intention of the axiom to 
assert a predicate of A and B as one, but to declare a relation 
between them. The distinction between the collective and the 
distributive use of the terms is here in question and it is a form 
of the familiar fallacy of composition of elementary logic that is 
committed. 

The argument a fortiori, "A is greater than B," (( B is greater 
than C, " therefore, " A is greater than C/'has been offered as an 



ir -» Principles of Logic, pp. 349, 360. 



in; FOOTNOTES TO FORMAL LOGIC 

illustration of asyllogistic reasoning. This, however, may be 
expressed in the following valid syllogism. Major premise. All 
rases where, of three things, the firsl is greater than the second 
and the second greater than the third, are cases where the first 
is greater than the third. Minor premise. A, B, C, is a case 
where, of three tilings, the first is greater than the second and 
the second greater than the third. Conclusion. A, B, C, is a case 
where the first is greater than the third. 

Bere again a criticism has been raised similar to that which 
we have just examined in the case of the axiom of equals. It is 
true that these so-called asyllogistic forms of reasoning are not, 
when reduced to the syllogism, strictly formal. But neither are 
they strictly material. From the two propositions li A is the son 
of C," and "C is the son of D," we may infer that "D is the 
grandfather of A." This is semiformal. It is a valid infer- 
ence only to one who also knows the ''system of relationships." 
But granted this prior knowledge, the inference within this 
''system" is evidently formal and capable of reduction to the 
syllogism. The same is true of the other a fortiori arguments. 



CHAPTER VIII 

NOVELTY AND IDENTITY IN INFERENCE 

I 

I find deplorable disorder and obscurity in current discus- 
sion concerning novelty and sameness, difference and identity, 
objectivity and subjectivity, independence and dependence in 
judgment. Some of these difficulties we met in the previous 
essay. I wish now to call attention to some further related 
problems. 

The New Logic asserts that the uniqueness of any mental 
fact is always of vital importance for some specific purpose ; 
that in truth, its uniqueness or individuality is driven in upon it 
from out of that external purpose. We have, here, a new and 
revolutionary definition of essence. The essence of the fact 
depends for its essential essence (if one may be permitted such 
reduplication ) upon the varying purpose to which it may be 
put. In other words there is no essence in the traditional sense, 
since the fact has no individuality, no character of its own. 
This doctrine, when applied without reserve, leads inevitably 
to the conclusion that there is no stability within the states of 
consciousness — that there are no laws of thought. And this 
issue the pragmatist accepts not reluctantly, but even more joy- 
fully than the ancient sceptics. In so far as we must take a risk 
in judgment, each situation is a law unto itself. The old ideal- 
ists uphold the law that there shall be law. The new theory 
recognizes only one law, namely, the law that there shall be no 
law. However, as we saw when discussing the nature of judg- 
ment, no idealistic theory of predication denies the novelty that 
comes with the predicate. Some risk we do take, and must take. 

[147] 



Ms FOOTNOTES TO FORMAL LOCK' 

But something over and above risk there must be in every judg- 
ment. That which enables the risk to know itself to he a risk is 

a stable principle of values. 

There are three possible views thai we may lake upon the 
question of the relation of stability to risk: Either there is all 
stability and no risk, as an absolute idealist might aver; or there 
is no stability and all risk as the pragmatist in my opinion is 
compelled to say ; or there is some stability and some risk as the 
dynamic idealist holds. If practical consequences are the sole 
test of truth — if the object-matter of judgment is brute force — 
then thinking is indeed pure adventure. But I submit that it is 
one thing to say that judgment is practical and hence riskful, 
and quite a different thing to say that there is nothing else to 
judgment but its utility and risk. 1 As Professor Hocking has 
said with such picturesque vigor: "Only he who has tried (or 
tried to imagine) a pure adventure knows that there is no such 
thing as a pun adventure; for when you have cancelled path, 
peak, sky, star, all distinguishable points in space, the adventure 
itself is abolished." 1 " 

We have sufficiently insisted that no relation can dispense 
with either of the two aspects the within or the between. A 
relation that attempts to exhibit identity without difference, or 
difference without identity is no genuine relation, since it omits 
one or the other of these two aspects. For this reason, as Bosan- 
quet has pointed out, no single judgment can exhibit a com- 
plete comparison ; a disjunctive judgment either implied or 
expressed is required. Every act of relating is an act of com- 
parison, and comparison always affirms the interdependence of 
identity and difference — it is redintegration. When we assert 



1 Cf. Bradley, Principles of Logic, pp. 18, 499. "The assertion we are 
to examine is not that practical influence induces us to judge, or results 
from ;i judgment: What is asserted is that judgment is nothing else 
whatever. . . . We do not mean to ask what sound performances of 
reasoning arc practicable, but what types of argument are flawless in 
themselves, without regard to the question if any one, or no one, can use 
them in his work." 

i" Meaning of Cod in Human Experience, p. xii. 



NOVELTY AXD IDENTITY IN INFERENCE L49 

that every judgment affirms or denies an identity in the midst of 
difference, and difference in the midst of identity, this must be 
taken to mean that we cannot begin with one alone and super- 
impose the other upon it as an after-effect. Both are present in 
one indivisible moment of consciousness. Although the differ- 
ence and the identity are concomitants in every judgment, the 
dominant emphasis may be shifted from one component to the 
other. Both may be quite indistinct in the first suggestion and 
the judgment may be aimed primarily to develop this inchoate 
distinction. Again one aspect in the presented correlation may 
be faint and the other vivid ; here the judgment will aim to 
reestablish the balance by emphasizing the weaker aspect. 2 

In his criticism of the three fundamental laws of thought of 
Traditional Logic, Hegel proved that the Law of Identity liter- 
ally interpreted, cannot possibly be an expression of the activity 
in any phase of a living judgment. If A is A, states a sheer 
tautology, it is no judgment. It proposes to say something, but 
ends by saying nothing. It is worse than idle breath, for it has 
not even asserted identity. The real Law of Identity "A is A" 
means that, whatever is true of A in one reference is true in 
another. 3 

The difficulty about the conception of identity and difference 
would be less puzzling if instead of the conjunction and, wo 
used some other word to describe the relation involved, for 
example, identity in or with, or because of difference. And is a 
highly ambiguous word. In Symbolic Logic it has been found 
very necessary to distinguish among its several meanings. For 
the present discussion the obvious warning is that and must not 



2 Bosanquet, Logic, I, 30. "As regards the affinity between Distinc- 
tion and Identification, they are obviously two sides of the same process 
and it is idle to ask which came first. So far as we can see, Consciousness, 
or at least Intelligence, must begin with both." 

3 Symbolic Logic which is rendering a most important service to exact 
thinking offers a definition of identity that is quite free from the per- 
plexing ambiguities that have beclouded it in the past. Cf. Russell, 
Principles of Mathematics, p. 20. "X is identical with Y if Y belongs to 
every class to which X belongs." 



L50 FOOTNOTES TO FORMAL LOGIC ' 

he taken to indicate mere juxtaposition. Ii' that were all the 
niul signified, then the whole, within which the identity and 
difference are aspects, would he no genuine whole: for either 

aspect mighl he removed and the other would suffer no change 

in meaning. The Limiting conceptions for ideiytity in difference 

are at the lower limit, pure tautology, at the upper limit, entire 
difference. But obviously these limits can never actually he 
reached by the judgment without sacrificing its essential char- 
acter. The judgment indeed, aims both at mere tautology, and 
mere difference, hut if it found its goal it would lose its life — 
the reverse of the scriptural experience of losing life to find it. 

In this modern indictment of the old Logic a most serious 
arraignment on all sides is made against the traditional laws of 
thought. But every argument against any one of these three 
laws always presupposes one or all of them. Every argument 
against identity assumes a principle of identity. The opponent 
of the Law of Identity must be standing upon a platform sup- 
ported by stable values when he assaults identity, otherwise his 
aim will be uncertain and he will miss the mark as widely as a 
howitzer anchored upon a drifting cloud. These attacks upon 
the law of identity are most surprising instances of oversight. 
Reason cannot commit suicide. A law of thought is reinstated in 
each attempt to remove it. The Aristotlian logic is the founda- 
tion of all logic even of those which attempt to overthrow it. 4 

No judgment affirms mere identity. If any collection of 
words should aim to assert identity they would not constitute a 
judgment, for as Hegel said, they would sin against the essential 



'Sidgwick, Elementary Logic: ''It is indisputable, e.g., that every 
.1 i>- .1. but tins leaves it quite uncertain whether any actual case of 'A' 
that we meet with is the genuine thing or not. Such a 'law' therefore 
has no application except on the assumption that we no longer need the 
Information that it is supposed to give. This kind of indisputability is 
common enough, and wo ean all manufacture as much of it as may 
(•out. -nt iiv.'" (p. L20.) ''.1 is prima facie ./. and not non-A, and clearly 
distinct from Ii. But if .1 ean !»<■ .1 for one purpose and non-A for another 
the supposed authority of these rules in application crumbles away to 
nothing. ' ' | \>. 157. 1 



NOVELTY AND IDENTITY IN INFERENCE L51 

characteristic of judgment. But, on the other hand, without the 
tacit assumption of identity, no affirmation or denial could ever 
be made. Sameness and difference are so inter-related that they 
are in reality different sides of the self -same content. Any two 
facts that fall within the same whole are alike and y«1 different. 
Nevertheless, although likeness is a fact and difference is a fact, 
we never mean to assert just the fact of likeness or the fact of 
difference. This is the puzzle which Professor Dewey has made 
the basis of his criticism of all conceptual logic. He says, in 
criticism of all such logics, "The rock against which every such 
logic splits is either that reality already has the statement which 
thought is endeavoring to give it or else it has not. In the former 
case thought is futilely reiterative ; in the latter it is falsifica- 
tory. " I shall attempt to show in detail, later that these two 
alternatives do not exhaust the possible points of view. We may 
answer both charges of futility and falsity by saying that the 
predicate is something which the subject already is or has, but 
which it was not known to be or to have prior to the predication. 
In his defense of independence the realist assumes a mind 
which is to know a totally independent and hitherto unknown 
object. He then gradually brings that object, so to say, toward 
the mind until the mind observing it, seizes it, and knows it. He 
admits that in any such act of normal thinking, when the object 
is known, that knowing of it causes it to enter into a new relation. 
But he emphatically declares that certain other relations the 
object retains, and that these are in no wise influenced by the 
new relation of the knowledge it has permitted to be set up. But 
now is it not an unwarranted abstraction by means of which the 
realist transcends the unity of knowing and being, and imagines, 
or conceives, or thinks an object independent of all knowing? 
When we separate being from knowing, reality from th ought, 
what is left is not just an independent unknowable something, 
but real non-being. Whoever declares that the objects of sense 
perception — or the objects of thought — are not in themselves as 



L52 FOOTNOTES TO FORMAL LOCK' 

they appear to us is making an assertion for which there is no 
Logical defense whatever. In order to pronounce the things in 
themselves other than, or independent of, the appearances, we 

must previously have compared the things as they are with the 
things as they appear. If this can be done then the independ- 
ence has hern disproved before we begin, and we are guilty of a 
negativt petitio. 

The realist in every age has put the burden of proof or dis- 
proof, upon the idealist. 5 He says that entities are independent, 
unless they are proved dependent. This is analogous to the 
familiar legal procedure of regarding a man innocent until he is 
proved guilty. That there is an important element of truth in 
this principle in legal practice I am not concerned to deny. In 
the law with which we are dealing, approximations to certainty 
merely, and the principle of the presumption of innocence is all 
we have. But in logical problems where rigorous demonstration 
is sought, it is a confession of weakness to give external evidence 
where internal proof should be forthcoming. 

The realist's definition of independence as equivalent to non- 
dependence is open to serious objections. In this definition he 
has failed to distinguish between the absence of dependence and 
the opposite of dependence. The realist admits that he cannot 
prove independence until the idealist has failed to prove depend- 
ence Let us accept his challenge and attempt to prove that 
there is ineffaceable dependence between idea and object. The 
realist asks us to go to experience for the confirmation of his 
doctrine. Objects in the world of matter he says are independent 
of one another ; so too are ideas in the world of mind. Up in 
Lake Superior, and quite on the bottom, he tells us, is a drop of 
water, and here are pages in a book. They are totally inde- 
pendent, are they not? The turning of the pages in no wise 
disturbs the essential being of that drop of water. And there is 



E.g., H. B. Perry, "Realistic theory of independence," Neiv Realism. 
(Ne-w York, hlacmillan, 1912), p. 99. 



NOVELTY AND IDENTITY IN INFERENCE 153 

Halley's Comet, winging its way through space preparatory to 
coming back to us again in seventy years. That, too, the realist 
says is independent of this page. But now when Ave enter the 
realm of possibilities, are these facts of our illustration so inde- 
pendent as they seem at first sight? The drop of water at the 
bottom of Lake Superior may come to the surface," evaporate, 
enter the atmosphere, be carried to this spot and fall upon this 
page and blur the ink — that is a possibility. Therefore, in 
criticism of New Realism the idealist insists that this possibility 
which is at the heart of the drop of water is already a part of 
its being, as it lies there at the bottom of the lake. The very 
possibility of its entering into harmful relations with my paper, 
prevents it from being regarded as an absolutely independent 
existence. It is an uncombatted possibility and therefore an 
actuality. Hence the idealist refuses to admit that even in our 
concrete human experience, we can ever find two physical objects 
which are so utterly independent of each other that no conceivable 
change in one of them can effect the other in any wise. 

But we need not rely alone upon this argument from the 
possibilities that lie inherent in the drop of water. That drop 
of water has, at this very moment, a relation to this paper — a 
relation that differs only in degree and not in kind from the 
relation which it would have to the paper if it were actually 
lying here now and blurring the words as they are being read. 
The realist would hardly venture to claim that space is more 
than a principle of differentiation. As I have already said, the 
realist declares that whenever we know any object (not our- 
selves) this object is existentially absolutely independent of our 
knowledge of the object. So that the ideas that constitute our 
knowledge may come and go, they may be true or false, and 
yet the object will remain forever what it was. In knowing the 
rest of the universe other than ourselves, we know something 
that is different from that knowledge, and because different is 
independent of that knowledge. And here is the novelty, the 
risk, the objectivity in judgment that can never be effaced. 






154 FOOTNOTES TO FORMAL LOGIC 

For further proof of this metaphysical doctrine of independ- 
ence, the new realist refers us to the mathematical theory of prob- 
abilities, where events are said to be mutually independent. In 
the throwing of dice, for example, each throw is independent of 

the others. lint again we should insist that when we look closely 
at all such illustrations of independence, we find that, in the last 
analysis, the objects so defined are always relative. This is 
pseudo-independence: we arc looking merely at special aspects 
of our objects. To use a crude but pertinent illustration — our 
fingers may be said to be separate and independent when we view 
them at their tips, and do not follow them back to their physio- 
logical connection at the palm. The two throws of the dice which 
the realist uses to support him in his metaphysical gamble in 
the search for independence, are connected in the general causal 
arrangement of our universe; they are really not wholly inde- 
pendent. We merely do not happen to know what the causal 
connection is. When we speak of pure chance we overlook these 
causal features and fail to observe that any two physical events 
occur in the same space, and in the same time. The parts of 
space and the moments of time, are perceptually, genuinely inter- 
dependent. Space and time are not principles of individuation, 
and nothing short of the individual can be regarded as genuinely 
independent. However far apart two objects are placed, they are 
still clutched in the enwholing grasp of space and cannot be 
totally indifferent to each other. Space is a principle by means 
of which things are "coupled apart." In the theory of probabili- 
ties, we do, to be sure, call two events that happen in the same 
space and in the same time independent events. What we mean 
is. qo1 that these two events are absolutely independent, but that 
there is an aspect in which we may treat them as independent. 
For certain purposes, we may ignore their interdependence or 
at any rate treat it as insignificant, and thus secure an apparent 
independence. 

It is precisely this pseudo-independence which the new realist 



NOVELTY AH D ID E X TIT Y I X I X /• E £ E X ( ) E 1 5 5 

has seized upon and magnified into a genuine independence. The 
realist's explanation of the process of knowing, as Bradley would 
say. is a "makeshift, a device, a mere practical compromise," 
which cannot be logically defended. From one point of view we 
have to take reality as many, and from another, as one — an 
ontological dualism and an epistemological monism. We insist 
on dividing reality for the purposes of existence, or to take it, if 
we wish, as indivisible for the purpose of knowledge. 

The idealist says that the alleged objects independent of 
consciousness are objective and independent only in the sense 
that they are the externalization of an internal constraint. They 
are what we must think, if thought is to be self-consistent. Our 
apparent success is won by a perpetual shifting of the ground, 
so as to turn our backs upon the aspect we desire to ignore. But 
when these inconsistencies are brought together, as in rigid Logic 
they must be, the result is an incurable discrepancy. The inde- 
pendent beings of which the realist speaks are beings that have 
no common features, no ties, no relations, or at any rate only that 
mysterious kind of relation which he calls mere dependence. They 
are separated one from the other by an absolutely impassable 
chasm. But such beings, we insistently repeat, cannot be in the 
same space or the same time, or be members of the same con- 
ceptual realm. They are false existences, and vanish at the touch 
of thought into the realm of non-being. They are not one, nor 
many, but just impossible nothings — just the drapery folded 
around the empty outline of ghosts of beings. 

The realist insists that real beings must be essentially and 
absolutely independent. In order to get such independent beings, 
he first declares that certain gaps or barriers are absolute. But 
he forthwith proceeds to make thought transcend these very 
barriers. He accomplishes this feat by an actual union of those 
parts of being, which in the first instance he attempted to put 
forever asunder. Realism attempts to divide the whai of an 
object from its that — the meaning from its existena — a vivi- 



156 FOOTNOTES TO FOSMAL LOCK' 

section thai must always prove fatal. It is true thai a psycho- 
logical dualism is implied in the very conception of conscious- 
Qi ss. Bui as we have seen earlier this postulated objectivity does 
not imply the ontological pluralism which the New Realism seems 
to demand. 

In the new realist's philosophy, quite closely related to the 
doctrine of independence and the problem of error, there is a 
third problem which is also one of the crucial test problems of 
the realistic metaphysics — the ancient problem of the one and 
the many, the whole and the part. One phase of this problem 
1 have already discussed in considering the doctrine of inde- 
pendence. The realist's explanation of the relation between the 
one and the many seems to me to be a complicated linkage of 
circular reasoning, in which the inquirer is continually deluded 
by an apparent approach to valid conclusions, and is yet all the 
while led back to the point from which he set out. The realist 
fails to reach any satisfactory solution of the problem of the 
one and the many, I venture to think, because he is applying an 
inadequate and imperfect conception of the relation of whole to 
part, and of the function of analysis and synthesis in judgment. 
In the world in which the pragmatist and the new realist first 
find themselves and beyond which they hold they can not go — 
the empirical, quantitative world — the parts of every whole, the 
elements of every multiplicity, stand in purely external relations 
to each other. This is one of the vital axioms of every form of 
realism. Every other principle or category that it employs, must 
conform to, or be a genuine expression of the fundamental char- 
acteristic of this phenomenal world, the mutual exclusiveness, the 
utter isolation of its elements. 

Bui in the world of thought, in the qualitative order, a funda- 
mentally different axiom is discovered. Consciousness is not a 
mere collection or aggregate of states, existing seriatim, each 
self-sufficient : but it is an organic whole, a genuine system, every 
pari of which has meaning only in so far as it is related to the 



NOVELTY AND IDENTITY IN INFERENCE 157 

rest. The new realist's problem of independence presents no 
difficulty if we accept Aristotle's definition of a true whole, that 
is, a whole such that if any part is modified or removed the total 
is entirely altered; for that of which the presence or absence 
makes no difference is no true part of the whole. In the deeper 
life of self -active mind, there is both multiplicity or diversity ; 
but it is the multiplicity or diversity that is not of parts, opposed 
to each other and constituting a whole by juxtaposition. In the 
organic whole of thought no part has an intelligible existence by 
itself in separation from the rest. Objects in the material order 
are by their very definition mutually exclusive. Each object in 
space lies outside of every other, and can be only externally 
related to them. But the independence of the elements in the 
thought system is the independence of that which although 
always limited is limited only by what is of the same essence with 
itself. The element in the scientific order is an element which 
declares its independence of all that lies without it. The element 
of thought, however, is an element which is ever discovering itself 
in that which apparently limits, or lies beyond it. 

II 

All vocabulary, and particularly English vocabulary, is defec- 
tive in words to designate the highest type of synthesis, that is, 
the synthesis which does not entirely efface the parts in the 
achievement of the whole. Also, we have no good single word 
to embrace the two aspects of the highest type of analysis, which, 
in winning its part is not totally disruptive of the whole. We 
greatly need in this discussion of the essential import of judg- 
ment what Philosophy in every language through all the ages 
has felt the lack, namely a single word to denote analysis in 
synthesis, or synthesis in analysis — the process in which an 
identity is preserved in the midst of difference. 

In the dialectic process, thesis, antithesis, and synthesis, 
namely, the positing of an object, the placing over against it its 



L58 FOOTNOTES TO FORMAL LOGIC 

negative, and then the reconciling of the two, vocabulary follows 
thought with an abundance of adequate words up to the second 
stage. Language is rich in words that distinguish the first two 
stages, thesis and antithesis; affirmation and denial, inclusion and 
exclusion, and their many synonyms and antonyms cover satis- 
factorily all of the various shades of meaning of the first two 
steps in thought's movement of increasing complexity. But, 
when we pass to the third stage of synthesis and think in terms 
of a genuine reconciliation of a concept with its negative, 
Language refuses to follow, or at any rate fails to provide a new 
and unambiguous word to denote 1 the essential characteristic of 
the complex thought process of this third stage — the stage of 
higher synthesis. The word which seems most nearly to express 
the double-acting character, the analytic-synthetic or synthetic- 
analytic process, in all judgments, or is constriction. As Bosa li- 
quet says: "The process of construction is always that of ex- 
hibiting a whole in its parts, an identity in its differences; that is 
to say. it is always both analytic and synthetic." 

On the higher level of synthesis, when we attempt to exhibit 
the results of reflective insight, we express ourselves imperfectly 
by circumlocution. If we are pressed for a single term to describe 
the third stage, we invariably employ the same words to designate 
the synthesis, or reconciliation of the thesis with its antithesis, 
that we have already employed to designate the thesis. This has 
given rise to endless confusion and misunderstanding in philo- 
sophical discussions. In the time-series, for instance, we posit 
as thesis is, then over against the is, we place its antithesis, was. 
lint now. when we are called upon to reconcile the two, when we 
comply with the inevitable demand of thought to discover what 
thesis and antithesis here have in common, we find not a third 
new word, but one of the two already employed, namely, is. In 
like manner, necessity and contingency are synthesized by neces- 
sity: the one and the many by the one. We generally mark the 
distinction, by capitalizing the one word in the position of 



NOVELTY AND IDENTITY IN INFERENCE 159 

synthesis. Or by way of explanation, we say that necessity is -a 
higher necessity which is the reconciliation of itself with the 
contingent ; or that unity is a higher unity which is reconciliation 
of itself with the many. The distinction between these two mean- 
ings of is, we find illustrated in the sentence, "Before Abraham 
was. I am." 

Of all our English synonyms of analysis and synthesis, the 
words differentiation and construction, best bring out the revers- 
ible and transitive character of the process. Any process of 
genuine construction always exhibits the final whole in and 
through its parts. It sets forth an identity in the midst of its 
difference. That is to say, as Bradley. Bosanquet and other 
recent writers have pointed out, it is always both analytic and 
synthetic. In any discussion of the interrelationship between 
analysis and synthesis it is important to distinguish between 
perceptual synthesis of parts into a whole in space and time, and 
conceptual synthesis of parts and whole in a non-temporal order. 
The result of the former process is always a mechanical, purely 
quantitative aggregate. The mathematician has ever had a clear 
conception of this interdependence of analysis and synthesis. His 
terms, integration and differentiation, are always employed in full 
view of the vital correlation of parts and whole. It is mani- 
festly impossible in the non-metrical reaches of geometry to think 
of this relation as one subsisting between parts and whole without 
confusion, because of the quantitative connotation of the terms 
part and whole as we ordinarily employ them. The mathema- 
tician has therefore wisely come to prefer the terms clement and 
system. Moreover, in describing the process of integration, he 
is careful to point out that in the complex entirety into which 
the elements have been combined, the elements are never impotent 
and indistinguishable. And conversely, in the process of dif- 
ferentiation into elements the system is never dismembered or 
multilated. 

The doctrine that a proposition is analytic when the predicate 



L60 FOOTNOTES TO FORMAL LOGIC 

is a genus or differentia of the subject, and synthetic when the 

predicate is a proprium, or accuh us, is maintained by Welton. 
This view obviously defines in a circle. It presupposes that we 
can distinguish between the accidental and the essential attributes 
of the subject, without invoking the assistance of the very con- 
ception of analysis and synthesis which this distinction is called 
upon to define. If the so-called accidental attribute is accidental 
in the literal sense of the word — if it has drifted in upon the 
subject like a snowtiake out of an unknown sky — then it is not 
even a synthetic judgment, it is not a judgment at all. It is 
worse than sheer falsehood, it is empty breath. However, if 
instead of the terms accidental and essential attributes, we use 
the terms external and internal meanings, we may discover a 
sense in which we can properly speak of analytic judgment as 
the explication, or determination of internal meanings, and 
synthetic judgment as the implication or determination of 
external meanings. But then, we should be obliged to return to 
the view for which we are here contending, that analysis and 
synthesis are inseparable, correlated aspects of every act of judg- 
ment. But it should be pointed out again that on this view the 
so-called accidental attributes or external meanings are not so 
accidental and external as at first sight they appear to be. 

The problem of the true import of judgment rests back finally 
upon this distinction between external and internal meaning. If 
we are to rescue judgment from the fatal paradox of being either 
false or idle, we must show that it is possible for the subject to 
have an internal meaning consistent with an external meaning 
brought to it by the predicate. Let us take any diyadic relation 
in a pluralistic universe. Let us assume, for example, that A 
and B are two minds or souls (Kantian ends), in such a pluralis- 
tic universe. .1 lias its internal meanings, namely, a, b, c, d, etc., 
and likewise its external meaning m, n, o, p. But on closer 
analysis it is discovered that these external relations m, n, o, p 



'■Manual of Logic, p. 104. 



NOVELTY AXD WEXTITY IX IXFEEEXCE 161 

are only the demands that are made upon A by B and these 
demands of B are B's own internal meanings, which are pre- 
cisely the aforesaid m, n, o, p. And in the same way B's external 
meanings will be a demand made upon B by A through its 
internal meaning a, b, c, d. In short, A 7 s external meanings are 
B 's internal meanings ; and vice versa, B 's external meanings 
are A's internal meanings. This logical doctrine, thus expressed 
symbolically is analogous to the definition of a true person in 
explanatory ethics. There too, the true insight is reached by a 
reciprocal determination of internal and external meanings. A 
person is being endowed with rights (internal meanings) that are 
inalienable, and duties (external meanings) that are absolutely 
binding. 

It must be observed that we deal with the same reality whether 
we approach it analytically or synthetically. This true insight 
into the real nature of analysis and synthesis in judgment settles 
finally, in my opinion, the much debated question whether the 
analytic judgment is really a judgment, that is to say, whether 
it is not in the last analysis idle; and the correlated question, 
whether the synthetic judgment, which is supposed to bring 
novelty in the predicate is not false. The subject is indeed given 
to us by one act of analytic attention, and the predicate by 
another. But to know the parts and to know the whole separately 
is not the same as to know the parts in the whole, or the whole 
containing the parts. 7 

Now it must be confessed that it is difficult to tell, in the 
analytic judgment precisely where its latent synthetic aspects 
begin to operate, and, in the synthetic judgment, it is difficult 
to tell at precisely what point the analysis begins. But I believe 
that careful psychological study of the thinking process would 



' Cf . Bradley, Principles of Logic, p. 447. "Unawares then we strive 
to realize a completion, single and self-contained, where difference and 
identity are two aspects of one process in a self-same substance, and 
where construction is self-diremption and analysis self-synthesis. This 
idea of system is the goal of our thoughts." 



FOOTNOTES TO FORMAL LOGIC 

show thai we often reverse the process several limes in a single 
judgment. We find an analogy in the physical world in the 
solution of the familiar Japanese puzzles. We often take ou1 

several sticks and then restore them to their respective positions 
in order to make sure that we may in the end bring the pieces all 
together again. So too, in pursuing an unknown path through 
the woods, we glance back often over our shoulders in order that 
the patli may be familial- on the return journey. 

As I have already remarked, of all our English synonyms for 
analysis and synthesis, differentiation and construction, or inte- 
gration seem best to bring out the reversible and transitive char- 
acter involved. Any process of genuine construction, always 
exhibits the final whole in and through its parts, as many genera- 
tions of idealists from Plato to Hegel have taught. It is both 
analytic and synthetic, therefore not just idle nor yet false. 

Among the various attempts to preserve for analysis and syn- 
thesis separate and entirely independent functions, that which 
rests upon the distinction between ground and cqnsequence has 
had many defenders. s It is maintained that whenever thought 
follows out a premise to a conclusion, or passes from cause to 
effect, the process is synthetic. But when the movement is in 
tin 1 reverse direction, namely, from consequence to ground, or 
effect to cause, the process is analytic. But obviously this view 
presupposes a transformation of the judgment in which its essen- 
tial uon-temporal character is disregarded. The relation of cause 
to effect, of ground to consequence, is a transitive and reversible 
relation. This reciprocal relationship is the vital characteristic 
of inference and judgment, and even of conception. In the 
relation of cause and effect, the cause is quite as much condi- 
tioned by the effect as the effect by the cause. This basal truth 
is continually overlooked in the instrumental theories of judg- 
ment. And the fallacy when carried on into the discussions of 
mediate inference causes endless confusion. 



»Cf. Metlone, I ntroductory Text-Book of L<><j'ic (ed. 2; London, Blacks- 
woo, I. l^itr, ,, p. 99. 



NOVELTY AND IDENTITY IN INFERENCE 16.1 

Subject and predicate, premises and conclusion, are together 
m the mind: on the printed page they are necessarily spread out 
seriatim. The proposition and the syllogism are in time, but the 
judgment and the inference, of which they are the outward 
expressions, are not in time. The judgment is not transition 
from subject to predicate, nor is the inference a transition from 
premise to conclusion. The parts of the judgment do not follow 
each other like the parts of the proposition. The relation is not 
merely lid wan two mental states, but is within a single enwhol- 
ing mental state. This single idea within which the elements of 
the judgment are held, not only permits but compels a transitive, 
reversible relationship between those parts. 

The presented facts which constitute the subject in the judg- 
ment contain two groups of elements, those which are explicit 
in the primary apprehension or perception and those which are 
implicit. 1 " Now the analytic judgment, is on the one hand, 
overtly the explication of these implications, and, on the other 
side, tacitly the synthesis of these same elements. The word 
analytic with its usual connotations as I have pointed out, is 
incompetent to exhibit this redintegration in the so-called analytic 
judgment — overt introspection (inward looking) with tacit retro- 
spection (outward looking). We likewise discover in the syn- 
thetic judgment the same essential dual process. The only differ- 
ence here is, that the group of presented facts, which again takes 
its place as the subject in the judgment, is now seen to be a con- 
stituent element of the whole which in the primary apprehension 
was implied. This larger whole now becomes implicit; it is dis- 
covered that the subject which in the primary apprehension 



'•' This is the now familiar doctrine, so long and so ably defended by 
Bosanquet. The essential concomitant- y of the parts of judgment had 
of course, been pointed out many times before, in the history of Logic, 
but no one had ever insisted upon the principle with such repeated 
emphasis. 

11 It must be admitted, of course, that there is some difficulty in 
speaking of these elements as being implied in the original datum. The 
enormously complicated question of the meaning of implies is here involved. 



L64 hOOTXOTKS TO FORMAL LOGIC 

seemed Bingle and isolated is in reality correlated with at least one 
other group of elements into a Larger concept, or idea. Thought 
is continually bringing together at one moment the result of the 
abstraction of a previous moment. Thought begins with a whole 
— with reality in some sense grasped as an entirety. It then pro- 
ci eds to disperse this whole by analysis (not a complete dispersion 
however) ami then gat Iters the dispersed elements into a whole. 11 
We first "grasp the sorry scheme of things entire," then "shatter 
it to hits" and finally "remold it nearer to the heart's desire." 
A vital question now arises which Professor Dew T ey asks as 
follows: 12 "Why and how should perfect, absolute, complete, 
finished thought find it necessary to submit to alien, disturbing, 
and corrupting conditions in order, in the end, to recover through 
reflective thought in a partial, piecemeal, wholly inadequate way 
what it possessed at the outset in a much more satisfactory way?" 
But no serious idealist has ever been willing to admit that thought 
is as Dewey says, perfect, absolute, complete, and finished, before 
it has submitted to these apparently alien, disturbing conditions 
of judgment. It is not truly itself until it has discovered itself 
by passing, in a piecemeal fashion, through these seeming foreign 
conditions. This reflective process through which thought passes 
is not partial and inadequate ; it is the highest type of adequacy, 
namely, self -completing adequacy. You may try to condemn 
thought by calling it finite, relative, conditioned, imperfect, frag- 
mentary, since it is obliged to reconstruct reality by the device 
of judgment. In fact thought will join you in such a condemna- 
tion of itself ; but forthwith it produces from within the principle 
of its own self-perfection, by means of which it escapes from all 
of these self-imposed limitations. 



n Bradley has expressed this thought with his usual clarity and 
vi^or: "Analysis is the inward synthesis of a datum, in which its unseen 
internal elements become explicit. Synthesis is the analysis of a latent 
whole beyond the datum, in which the datum becomes explicit as a con- 
stituent element, bound by interrelation to one or more elements likewise 
constituent." Principles of Logic, p. 432. 

i- Logical Theory, p. 45. 



NOVELTY AXD IDENTITY IN INFERENCE 165 

Iii this discussion of the essential identity or at least the 
inseparable correlativity between analysis and synthesis, it is 
important to point out that the thought process exhibited in 
the relationship is one that always involves a triadic relation. I 
have already spoken of the duality of the relation but there are 
really three centers of separate attention. Analysis not only dis- 
tinguishes each element from the other, but also distinguishes 
each element from the whole. Also, when we read off the con- 
tent in the reverse direction, we find that synthesis so combines 
parts into wholes that the relations of the whole to each of the 
several parts, as well as of the parts to each other is never obliter- 
ated. Both analysis and synthesis establishes and maintains 
relations, but the relations here involved, I repeat, are essentially 
triadic, because every such relation involves both a between and 
a within. If the relations between two terms A and B, be 
expressed by R, then W would express the whole within which 
this relation is embedded, and R, the relation between A and M 
and also between B and M. The triadic relationship would run 
thus: A-R-B, A-R-M, B-R-M. While it is true that every 
judgment is both analytic and synthetic, Ave may yet assert 
(without yielding any essential part of the position we are 
advancing), that judgments of sense are synthetic and judgments 
of reason are analytic. The former do transcend the sense-pre- 
sented content ; they are more than simple apprehension. The 
latter always start with a whole or system, in which differences, 
already existing are further developed. 

Some writers have attempted to overcome the apparently 
vitiating tautology of the analytic proposition by making two 
classes of so-called verbal proposition — analytic and synon- 
omous. 13 In the one class the predicate aims at an exposition, 
or analysis of the intension of the subject, for example, Bodies 
are extended, An equilateral triangle is a triangle having three 
equal sides. These are regarded as the true type of what should 



!3 Cf. Keynes, Formal Logic, p. 50. 



L66 FOOTNOTES TO FORMAL LOGIC 

be called analytic propositions. They arc uever tautologies or 
hare identities and therefore may never be condemned as trivial. 
Even where the exposition of the intension of the subject is com- 
plete and the proposition becomes a definition, such propositions 
are still to he distinguished from the other group which Keynes 
calls '•synonymous. " In this class the predicate is not an exposi- 
tion of the intension of the subject; it gives information only in 
regard to the external reference of the subject or is its dictionary 
synonym, for instance, Tully is Cicero, or A story is a tale. This 
is a distinction that for practical purposes may be useful, but it is 
hardly defensible theoretically. The class of synonomous propo- 
sitions that is here interpolated, is provided with no precise line 
of logical demarcation from the analytic and the synthetic class. 
A third class is not strictly needed. Even in those propositions 
where subject and predicate are both singular terms we may, 
and in truth, must regard the judgment, w T hich the proposition 
expresses as an equating of synonyms, as conforming to the funda- 
mental principle of all judgment, namely, the assertion of an 
identity in difference. Neither in judgment nor in inference 
can thought pass from particular to particular ; for example the 
proposition this is that corresponds to no actual judgment any 
more than this is this. We do violence to the real judgment when- 
ever we attempt to interpret it in any other way than that of a 
universal, exhibiting itself in and through its differences. The 
challenge to describe these synonomous propositions as either 
analytic or synthetic can not be met, indeed, if it means that 
they are to be either one to the exclusion of the other. But they 
can all be described as analytic-synthetic. Even Tully is Cicero 
or A story is a tale are assertions of identity in the midst of a 
difference; we pass out beyond the judgment at the one link into 
bare tautology and at the other into falsity. 

The results on which we would insist may now be briefly 
summarized. The relation of judgment to conception is recip- 
procal. The judgment expands the conception and in expanding 



XOrELTT AND IDENTITY IN INFEBENCE 1(57 

enriches its meaning. It does this by adding new relations to the 
group of references that it already has. Every judgment asserts 
both identity and difference. An assertion that is merely identical 
is no judgment. So, too, if a judgment is merely synthetic, and 
no bond is perceived between the subject and predicate, that is, if 
the two are not seen to be embedded within a whole there is no 
real judgment, but only association. Every judgment purports 
to be both a unity and a multiplicity. If it did not. fulfil its 
purpose to exhibit an identity, it would cease to exist. But this 
external unity at which it aims is not inconsistent with endless 
multiplicity within. The content of judgment, though a single 
definite idea in any external reference, is when viewed interiorly, 
capable of manifesting itself in an endless variety of meanings. 
Judgment is a self-enclosing expansion, a unifying of the many 
and a multiplying of the one. The reality with which judgment 
is concerned is a whole, completely revealing itself in each of its 
parts. Judgment is a unity breaking itself up into a multiplicity 
and then reasserting itself as a unity. It is the highest type of 
redintegration. It is both true and false and neither. 



Ill 

The first of all the prerequisites for judgment is a world of 
reality different from, or at least distinguishable from the world 
of ideas. A judgment always claims to be true. It is idle to talk 
about judgment until we have distinguished between idea or 
psychical fact and the reference of idea to objective fact or 
reality. One of the purposes of these studies is to show how and 
why this distinction is made. This claims to be true, which is one 
of the several correlated factors in all judgment, might also be 
described as judgment's intrinsic necessity. It would also be 
equally accurate to speak of it as the objectivity in judgment. 
Objectivity in judgment is nothing else than its necessity. What 
we are obliged to think, through this self-compulsion of thought, 



FOOTNOTES TO FORMAL LOGIC 

constitutes its objectivity. These arc truths that the history of 
Logic has repeatedly been compelled to recognize. No one can 

understand thought as an instrument of conviction until he has 
studied it in its relation to its subject matter. There is an inter- 
structural correspondence between thought and facts. 14 Every 
judgmenl therefore has objectivity even if it has no object. And 
such a view of objectivity allows ns to say that the conditions of 
actual and possible thought do correspond with the conditions of 
actual and possible being, and that, therefore, what we think 
exists and what we can not think does not exist. 

Since judgment always refers to something other than itself, 
it has been maintained that Logic is the science of thought when 
engaged upon an object other than Logic. This is a doctrine 
which I think is entirely defensible although the common under- 
standing of it leads to all manner of contradictions. The living 
judgment, perhaps, can not become its own object and still live. 
The Hegelians have always held that immediate consciousness is 
self-contradictory. For them there is no such thing as the vivi- 
section of a thought. But, continuing this metaphor, may we 
not say that there can be a postmortem examination of departed 
thinking by its own resurrected self ? 

The attempt to make a distinction between the judgment of 
perception and cognitive judgment breaks down with any care- 
ful analysis of psychical facts. There is no difference in kind, 
on our theory, between perceiving and perceiving that I per- 
ceive, or between thinking and thinking that that is one of my 
thoughts. Idealism of every form declares that objects of 
thought, just because they are thought, have a different kind of 
existence from what belongs to them when they are not thought — 
if that may ever be. Mind is, in other words, in some sense 
creative. The realist says that the validity of thought depends 
quite as finally upon the object thought about, as upon the 



n On this point we are in cordial agreement with the instrumental 
pragmatist; we differ, as J have tried to point out in an earlier chapter, 
on the \v;iv in which the relation is read off. 



XOVELTY AXD IDEXTITY IX IXFEFEXCE 169 

thought itself. He contends for a fundamental distinction 
between idea and object. He grants the idealist's main conten- 
tion that certain objects of thought do not exist outside of the 
mind, but he denies that therefore the mind creates these objects. 
When reduced to its lowest terms and stripped of all unnecessary 
verbiage, there is, one fundamental difference between the old and 
new Logic. Every form of idealism has asserted that experience 
does create its object, that the self does beget the not-self. 

Professor Dewey 15 has stated in a very concise form what he 
takes to be ''the point of contact and hence of conflict" between 
idealism and instrumentalism. The significant sentence reads : 
''The idealistic logic started from the distinction between imme- 
diate plural data unifying, rationalizing meanings as a dis- 
tinction ready made in experience, and it set up as the goal of 
knowledge (and hence as the definition of true reality) a com- 
plete, exhaustive, comprehensive, and eternal system in which 
plural and immediate data are forever woven into a fabric and 
pattern of self-luminous meaning/' A liberal idealist could 
accept this statement by changing the one word ' ' self-luminous 
to "self illuminating." This would make the difference between 
static and dynamic idealism. Thought is not perfect but self- 
perfecting. Thought strives for something; it needs something 
apparently beyond itself; it is permeated with wonder, with 
curiosity, which points to a fundamental defect in its nature. 
But in this never-ending aim to be a whole, to be self -complete, 
thought is incessantly discovering that there is nothing genuinely 
outside of itself. If in this striving for self-completeness, it 
should actually reach its goal, thought as such would obviously 
be destroyed. Thought's aim is to get hold of an object as a 
whole, the separate elements of which it already has. Now it is 
precisely this self -completion of thought beyond itself, which 
constitutes the object, the independent thing in every type of 
realism. In the subject-object relation, then, the expected self- 



is Experimental Logic, p. 22. 



170 FOOTNOTES TO FORMAL LOGIC 

transcendency of tin subject constitutes the object. Thought 
moves by means of relations toward a goal which lies beyond 
relations. The attainment of its goal by transcending relations 
would be the annihilation of thought. 

What Idealistic Logic discovers when it reaches final reality 
is a whole in which distinctions can be made and are made, but 
in which the genuine diversity — the bona tide independence — 
demanded by the New Realism does not exist. The position of 
modern realism on this central question of Logic can be stated 
briefly, but with rough justice thus: The perception of relations, 
which is the fundamental characteristic of the judging conscious- 
ness, is a self -contradictory but necessary blending of the one 
and the many, unity and variety. This relation is unique, 
logically indefensible and undefinable. Consciousness, it is 
asserted, has the undeniable feature of immediacy. The idea 
has hold of its object. This establishes continuity. But equally 
undeniable is the characteristic of self-dependence, or independ- 
ence. The terms which consciousness unites in the relating 
activity of judgment are, in truth, given to it, and not actually 
made by it. This given reality with which it deals is therefore 
essentially pluralistic. 

But I submit that at this point the modern realist has allowed 
his dialectic to halt. He has stated only half of the whole truth. 
The other half is the indisputable fact that this cognition which 
binds together the many, represents at its center an original 
onderived whole. It is a synthesis, a unity, which is not made 
by the original differences in the presented facts, but is placed 
upon them. The whole is not just composed of its parts, it con- 
stitutes them and is legislatively sovereign over them. Now it is 
this characteristic and apparently paradoxical feature of thought 
that neither the Instrumental Logic nor the analytic realism 
srems able to surmount. Thought does aim to retain these two 
features, unity and plurality, and at the same time weld them into 
a higher harmony. It strives to reach an all-embracing whole 



NOVELTY AXD IDENTITY IN INFEBENCE 171 

which shall not in any way conflict with the immediate elements. 
It therefore bestows upon its elements a kind of independence. 
But at the same time it seeks for elements that shall be sub- 
ordinated to the entirely independent (i.e., superior) whole. 

There is, then, this paradoxical fact about thought and its 
object ; they are two and yet can never be studied in isolation. 
Thinking, is always thinking about something, and thought can 
never be divorced from this postulated objectivity and treated as 
pure subjectivity. This point, which has now so often been 
insisted upon, seems invariably to be ignored by realists and 
pragmatists in their criticism of idealism. Thought can never be 
investigated in abstraction from its objective reference. Such 
a view as I am here stating, concerning the relation of subject 
to object, may when taken at its face value, appear to be a con- 
cession to the central thesis of pragmatic logic, namely, that the 
form of thought must wait upon its matter. On this view, it will 
be asked, how can Logic be regarded as the study of the forms 
of thought? If the form and the matter are thus inseparable, 
inter-related in each concrete instance of thought, how can there 
be any form in general? I cannot think the answer to these 
questions and the justification of Formal Logic is far to find. 
Just as we can inquire into the laws of gravitation without 
examining all the objects that have ever fallen, so we may study 
the laws of thought without studying all the objects that may 
conceivably be discovered at the other end of the subject-object 
relation. 

IV 

There now arises a question of singular gravity, the central 
question of speculative Logic through all the centuries. That 
portion of thought's content which constitutes its meaning or 
external reference as distinguished from its existence, we have 
insisted, is a systematic totality. This is what we mean when 
we speak of the world of all possible objects of thought. How 



L72 FOOTNOTES TO FORMAL LOGIC 

far into this realm of objective reference must thought go before 
it can claim finality for its deliverance 1 One school of philosophy 

has held that perfect validity of thought would require perfect 
insight into the objective system. Bosanquot has said, "Ulti- 
mately nothing can be rightly known without knowing all else 
rightly." Others insist that we have some knowledge that is in- 
complete and yet perfect, and that we can pronounce judgments 
that are not subject to future revision. The agnostics, from the 
ancient sophists to the new realists have declared that never in 
the growth of knowledge do we reach a stage at which we may 
say. "The evidence is now all in, and the judgment of finality 
can be pronounced. We do not have perfect control over the 
object ; if we did it would cease to be an object. It is just this 
alien character that constitutes its objectivity. 

The Idealists have always given a decisive affirmative answer 
to this fundamental question; we do have perfect knowledge in 
part. Professor Hocking has defended this cardinal tenet of 
traditional idealism with impressive clarity of illustration. He 
pointedly tells us that unfinishedness is not itself a blemish, and 
says: "There are tolerable and intolerable kinds of unfinished- 
ness. A thing is properly unfinished w T hen it is finishable; and 
it has an identity that finishing will not change. Let an artist 
sketch a face with all conceivable haste and roughness. The 
unfinishedness is justified if only it is a thing, if only it has a 
character and a significance that all later finishing does but 
develop without displacement or substitution." 16 

The truth about our fragmentary thought, as it comes to us 
by the pathway of experience, is not that it is imperfect or incon- 
sistent, but that it is incomplete. It is indeed not adequate to the 
whole of reality, hut what it does deliver is genuine. From its 
one shore, thought bridges the gulf between it and reality by 
pushing out cumulative cantilever arches, each firmly and 
unchangeably anchored. It is not a pontoon bridge whose units 



"•The Meaning of God in Human Experience (New Haven. Sale 
University Press, 1912), ]>. x. 



XOrELTT A XD 1 BE X TITY IX IXFEEEX CE 173 

are swayed by the dashing tide, and whose mooring to the shore 
may require to be changed as its length increases. 

Actuality, which is just one aspect of objectivity, is the 
necessitated possible. This is Bradley's well-known view. The 
most fundamental law of thought is the law by which we assume 
that every isolated, unique possibility is also real. In other 
words, the uncombatted possible is the actual. This law, cannot 
be exhibited as the operation of either analysis or synthesis or 
both correlated, and yet it is a normal, universal way of thought's 
functioning. Every time reality presents itself as a subject for 
a possible judgment, and reaches out among the possible predi- 
cates, that one of these possible predicates which finally stands 
alone, either because there are no other possible predicates, or 
because other competing possibilities have been rejected, is appro- 
priated by the subject. This appropriation elevates the predicate 
from possibility to actuality. We may not be cognizant of the 
operation of this law, and may indeed when our attention is 
directed to its operation, be inclined to disclaim it, but we 
nevertheless do finally and always owe allegiance to it. Instead 
of saying that the mind selects one of the several alternatives 
and so depresses the others, it would be more accurate to say 
that the several impossible possibilities having been destroyed 
the single uncombatted possibility stands self-affirmed. The 
actual, the real, the object, is that which resists the subject. A 
thing has objectivity if it exhibits, in its own name, any force 
or necessity. 

This doctrine again must not be confused with the teaching of 
pragmatic Logic, which at first sight it resembles. The Logic 
of Pragmatism tries out the various possibilities and tests truth 
by acting as if. When the question arises whether the new- 
possibilities which are applying for acceptance are true, or real 
we must test them, one by one, by acting as if they were true, 
and accept in each instance those that work in with the old. But 
this pragmatic test of truth, as I have shown elsewhere, assumes 



17 1 FOOTNOTES TO FORMAL LOGIC 

the rationality of the Old, and asserts thai the new which works 
in with this, is true. Of course, if we start with an original 
matrix of truth, then whatever tins accepts as true, will be true, 
and whatever it rejects because it does not work, will be false. 
Hut the Pragmatic Logic is incapable of endowing this original 
mass with the essential truth necessary to make the principle 
as if operate. Bradley's doctrine does on the surface seem 
identical with the pragmatic test — wherever a suggestion is not 
rejected by the facts with which we start, or again by some other 
suggested quality, and we are left not with disparate possibilities, 
but with one uncombatted maybe, that suggestion must always 
be taken as fact. The facts with which the pragmatist starts are 
not possessed of universality ; with Bradley they are. He says : 
"The striving for perfection, the desire of the mind for an 
infinite totality is indeed the impulse which moves our intellect 
to appropriate everything from which it is not forced off." 
Possibility is a kind of necessity, and consequently there is no 
difference in kind between the problematic and the apodeictic 
judgment. A thing is possible when at least one of its conditions 
is present, and actual when none of its conditions is absent. 



V 

As a typical illustration of the sceptical attitude of the new T 
movement toward reality, objectivity, or necessity, we may quote 
two Protagorean passages from Professor Sidgwick: "Absolute 
truth is never attained but that further improvement is always 
possible." ''There is no need to make any pretence of securing 
infallibility of judgment, even in a single instance. If Absolute 
Truth means Truth as it would appear to a superhuman mind, 
how can we presume to have reached it? Or, if by any chance 
we did reach it, what means would we have of distinguishing 
between it and the truth that merely suffices for human pur- 
.'*' ,: The modern idealist always replies to this agnosticism 



Elementary Logic, pp. 123, 170. 



XOVELTY AXD IDEXTITY IX INFERENCE 175 

in the spirit of Socrates' reply to the ancient sceptics. Knowl- 
edge has this peculiar paradox about it : We have a criterion 
of truth — we know what valid knowledge ought to be; and yet 
we can never in our practical experience reach any such knowl- 
edge as is guaranteed by this criticism of validity. 

Professor Sidgwick's own statement that "absolute truth is 
never attained but that further improvement is always possible ' ' 
is itself an illustration of this "self -perfecting" criterion of 
knowledge. When we assert that further improvement is possible, 
we imply a criterion of stable values, or else the word improve 
ment does not mean what it purports. Improvement and pro- 
gress are indeed dignified words but no one has any right to use 
them, either in Logic or Ethics, who does not admit something 
absolute, some definable standards of value. The modern enemy 
of Traditional Logic and Ethics declares that knowledge is 
limited to a world of comparatives, whose superlatives are never 
in sight. We do not know the beautiful, the true, the right, and 
never can know them, for there are no esthetic, logical, or ethical 
standards. We simply have knowledge of the first two degrees, 
namely, the good and the better ; and from these as a base we 
must triangulate our journey. But in full view of all the many 
indictments the idealist still asserts, with renewed emphasis, 
that any genuine improvement implies direction, a goal. If we 
are in the least degree uncertain about the goal, we must in the 
same degree be uncertain about the improvement. Improvement 
is not measured in terms of mere movement. We can be much 
"on the go" without making any improvement — witness many 
aspects of our present civilization. In other words, briefly, 
improvement is estimated not by the distance one has gone, but 
by the distance one has yet to go. 

"There are probably few people at the present day," says 
Sidgwick. "who would confess to holding that the general rules 
by which our thoughts and our lives are mostly guided deserve 
to be applied through thick and thin." 18 One may agree with 



18 Elementary Logic, pp. 160, 161. 



L76 FOOTNOTES TO FORMAL LOCK' 

this statement bo Ear as the word "mostly" is concerned, and 

admit thai humanity docs depend for its practical faiths very 
largely upon insights thai are transitory, partial and for the 
most part subconscious. We act most often before the arrival 
of certainty and under the guidance of shifting standards. But 
surely Professor Sidgwick must believe in some things that abide. 
Can tlic solemn agreements among men never be final? Is there 
no pact that deserves to be applied through thick and thin? If 
not, then the most pragmatically consistent of the nations in the 
greal world -war is Germany. A treaty is indeed merely a scrap 
of paper to be respected only so long as it is convenient to 
respect it. 

Another illustration of how the pragmatist fails, it seems to 
inc. to grasp the idealistic notion of a self-perfecting control of 
the object, I may quote from Mr. H. 0. Knox: "We simply 
deprecate as futile the assuming of a transcendent and absolute 
reality as the standard to which our actual judgments are to 
correspond. For (a) if an absolute standard were available for 
actual comparison the comparison itself would be purely super- 
fluous. We should already be de facto in possession of absolute 
and infallible certitude. And (b) to say, that reality is trans- 
cendent is simply to say that it is not available as a standard at 
all" 19 This is clearly a restatement of the ancient paradox of 
the apparent futility or idleness in judgment which I have 
attempted to answer in the chapter on "The Import of Judg- 
ment." 

All necessity is in the end conditional, since every must be 
rests back upon a because. All objectivity is in the end sub- 
jectivity since reality is continuous and since the thinking self 
'a/aid Cartesianism) is the initial indefeasible reality. If the 
object lay genuinely outside the system of thought it could never 
be reached by thought. The knowing process does not involve 
a transition from subject to object; it consists in a progressive 



■• Mnul. ,,. s., XVI IT (1909;, (\wi. 



XOVELTY AND IDENTITY IN IXFEEENCE 177 

analysis and development of the objective aspect of the total con- 
tinuous reality. This view will seem to resemble Professor 
Dewey's account of the subject-object relation. He writes: "The 
distinction between subjectivity and objectivity is not one 
between meaning as such and datum as such. It is e specifica- 
tion that emerges, correspondent^, in both datum and ideatum, 
as affairs of the direction of logical movement." 20 There is, 
however, an essential difference between this position and that 
which I have now urged from several points of view in these 
pages. A cross-section of the stream of consciousness in Pro- 
fessor Dewey 's doctrine, it seems to me, does not raise the vital 
question of the correspondence or coherence in the longitudinal 
section of the thinking process. No matter how completely we 
may seem to explain the subject-object in any situation as the 
meeting point of converging forces, we still need the help of a 
principle outside of the pragmatic movement to explain the 
identity that persists in the spatial or temporal series. Spatial 
judgments are far from being as particular or factual as on the 
surface they appear to be. Every here contains a there and 
hence it is never a particular. Spatial references in judgment 
are always universal. There is never given to thought a genuine 
this or that, but always thisness and thatness. We may say the 
same of our temporal judgments. It has justly been maintained 
that every present includes a past, and therefore no temporal 
judgment can be strictly particular. 



20 Experimental Logic, p. 55. 



